Two-sided dynamics in duopolistic ridesourcing markets with private and pooled rides

Abstract

Network effects in ridesourcing suggest fragmented (multi-platform) markets produce worse rider-driver matches than monopolistic markets. This research addresses two key gaps: (i) understanding how fragmentation costs such as longer detours for travellers, decreased driver income, and increased vehicle kilometres travelled (VKT) vary with market features and user attributes, and (ii) exploring conditions under which fragmented markets sustain. To this end, we propose an agent-based model accounting for day-to-day processes and within-day dynamics in markets with service providers offering private or shared rides. Amsterdam-based experiments reveal that two platforms can co-exist when ride-pooling is offered by just one of them, driven by differences in target demographics, or by both, due to negative network effects from detouring under limited demand. Fragmentation of the ride-pooling market yields 6.4% additional VKT. When both platforms offer (only) private rides, co-existence is feasible when a fraction of travellers and/or potential drivers engages in multi-homing.

Introduction

Ridesourcing platforms have revolutionised the taxi industry by leveraging the ubiquity of smartphones and mobile data to connect travellers directly with private drivers. Advanced real-time algorithms for matching trip requests and drivers adopted by these platforms allow for efficient pick-ups. At the same time, the outsourcing of vehicle and labour supply to freelance drivers can enhance the alignment between supply and demand levels. The platform business model allows ridesourcing providers to seamlessly expand from one city to others, which may explain why in numerous cities worldwide, ridesourcing service is offered by various platforms concurrently. For example, Uber and Lyft provide ridesourcing services in New York City, while Uber and Bolt offer similar services in Amsterdam.

As the efficiency of the matching of drivers and riders in ridesourcing services is intricately linked to the scale of the market¹, the overall system efficiency is likely to be smaller in ridesourcing markets with multiple service providers compared to monopolistic markets². This affects users through longer waiting, drivers through less productive work, platforms through lower market shares, and the general public through increased vehicle kilometres travelled (VKT), leading to longer travel times and higher emissions. In New York City, it was estimated that fragmentation of a market with only private rides (from hereon referred to as a ride-hailing market) leads to a 4–6% increase in the minimum fleet size required to serve all trips in case of two providers and 6–10% if there are three providers³. ^4,5,6,7 establish that market fragmentation costs strongly depend on context variables, including the number of service providers, the initial fleet size, trip density, the market share of ride-hailing and traffic speeds. While in Manhattan, for example, the increase in the minimum fleet size associated with market fragmentation (assuming fixed taxi demand) is estimated at just 2.5%, it is estimated at 8.5% for Singapore, 37% for San Francisco, 55% for Vienna, and even 67% for Curitiba⁵.

An important shortcoming of the aforementioned studies on market fragmentation costs is that they assumed fixed demand and supply per service provider, while in reality ride-hailing markets may be prone to developing towards a winner-takes-all equilibrium⁸. Kondor et al.⁵ highlight that smaller players (platforms) face a comparatively higher cost associated with market fragmentation. This could trigger a feedback loop where the declining service quality of the smaller platform diminishes its attractiveness to potential consumers and suppliers, further exacerbating the reduction in service quality. Ultimately, this cycle might lead to a scenario where the larger platform emerges as the sole provider in the market. As a consequence, monopolists could exploit their market dominance by raising fares and commission to the detriment of travellers and drivers.

Multi-homing behaviour by travellers and drivers can possibly prevent or mitigate potential undesirable consequences associated with ride-hailing market fragmentation⁹, i.e. the emergence of monopolistic markets or a suboptimal service when multiple platforms co-exist. Multi-homing enables both suppliers and consumers to use multiple platforms concurrently. Drivers can receive requests from various platforms, while travellers can check vehicle locations on different platforms or request rides from multiple platforms simultaneously, thereby increasing the likelihood that an idle driver is in the proximity of a pending trip request. However, there is evidence that multi-homing can impose substantial (financial and non-financial) costs on drivers¹⁰, explaining the mere 25% multi-affiliation among drivers in Chicago¹¹. It is plausible that such multi-homing costs also exist on the demand side, as evidenced by the 17% of ride-hailing consumers in New York City who use multiple platforms¹².

It is plausible that market fragmentation costs are even larger — and consequently winner-takes-all markets even more likely — in the provision of ride-pooling, compared to ride-hailing. The reason is that ride-pooling system efficiency is even more scale-dependent than ride-hailing¹³ given that pooling relies on compatibility in trip requests (to obtain acceptable waiting times) in addition to driver-request pairings (to obtain acceptable in-vehicle times). Passenger utility can either increase (shorter detours, occurring particularly when demand for ride-pooling is already high) or decrease (longer detours, particularly when demand is moderate) with demand for ride-pooling¹⁴. Ride-pooling fragmentation costs further depend on pooling thresholds set by the platform and the spatial distribution of trip requests¹⁵.

At the same time, markets with service differentiation between platforms, for instance, when one service provider offers hailing and the other one pooling, may be less prone to winner-takes-all equilibria¹⁶. These service types target different market segments: pooling serves cost-sensitive users, while hailing accommodates the preferences of time-sensitive individuals.

Previous research examining ridesourcing market equilibria following from competition among ridesourcing providers, including traveller and driver responses, has focused on three key areas. First, a substantial body of literature has delved into the intricate dynamics of pricing arising from the strategic decisions of competing service providers in the market^{8,11,17,18,19,20,21,22,23,24,25,26,27,28}. Notably, research by refs.^17,18 demonstrates that competition in the ride-hailing market may not necessarily lead to lower service prices as platforms compete for suppliers in addition to consumers. Second, multiple studies evaluate the impact of multi-homing in ridesourcing markets based on analytical models^{8,9,11,29,30,31}. Resulting from a trade-off between enhanced matching efficiency and increased platform pricing power (as platform competition is more limited) under multi-homing, whether multi-homing increases or decreases social welfare remains subject of debate without a unanimous consensus. Lastly, a separate strand of research examines ‘coopetition’ strategies, where competitors collaborate to mitigate matching inefficiencies in competitive ridesourcing markets^{16,32,33,34,35,36,37}. These studies investigate a range of strategies, including bilateral and centralised trading, as well as launching joint services with profit-sharing arrangements.

In determining ridesourcing market equilibria, previous studies substantially simplify interaction effects between supply and demand in the evolution of ridesourcing services, visualised in Fig. 1. First, previous works utilise aggregate matching functions for determining how double-sided market participation utilities depend on double-sided participation levels (relations marked (A) in Fig. 1), by which they neglect the spatio-temporal nature of within-day ride-hailing and ride-pooling operations. Second, macroscopic functions are applied for the reverse relationship, i.e. to establish platform participation levels depending on system performance (relations marked (B) in Fig. 1), by which they neglect crucial disaggregate, day-to-day processes in ridesourcing provision³⁸. This also applies to generic studies investigating competition among two-sided platforms^{39,40,41,42,43}.

Fig. 1

Conceptual representation of the interaction between supply and demand in the ridesourcing market.

We address the stated research gap with an agent-based model capturing both within-day ride-hailing and ride-pooling operations as well as day-to-day processes affecting market participation levels. In particular, our study has the following specific (interrelated) contributions:

• I. Day-to-day dynamics in the two-sided market: In our day-to-day model, we represent diffusion of platform awareness, tactical registration decisions and daily market participation decisions in consideration of imperfect information, i.e. following from learning from own and others’ experience. The day-to-day model enables exploring under which conditions initial differences in market shares between platforms — resulting from platform entry timing or random advantages — translate to winner-takes-all (or asymmetric) market outcomes. In addition, accounting for day-to-day processes in ridesourcing provision allows for establishing day-to-day variations that may occur in system performance in the market equilibrium, a feature that has not been commented on in previous research.

• II. Detailed ridesourcing dynamics with competition: We model the within-day interactions between individual service providers, users and drivers, accounting for their spatio-temporal attributes and possibly resulting in distributional effects. Specifically, the model represents platform matching, ride offer acceptance decisions and repositioning decisions, all affecting experiences with the platform and, consequently, market participation levels. In addition, accounting for drivers’ repositioning allows us to give a more complete picture of the effect of ridesourcing on the VKT.

• III. Ride-hailing and ride-pooling: In addition to modelling within-day operations exclusively for platforms offering private rides, we extend our analysis to incorporate ride-pooling services. This allows us to examine the likelihood of winner-takes-all markets in ride-pooling compared to ride-hailing, considering network effects in traveller pairing. We also explore market competition effects when one platform offers ride-hailing and the other offers ride-pooling, potentially targeting distinct user groups based on trip-related attributes, mode preferences, and socio-economic characteristics, the importance of which has been underlined by the results of ¹¹.

• IV. Single- and multi-homing: We account for multi-homing practices in our day-to-day and within-day models, i.e. (participating) drivers and travellers can be tied to a single platform or open to offers on multiple platforms. Contrary to previous works investigating multi-homing, our approach allows for investigating mixed multi-homing scenarios, i.e. scenarios in which some agents multi-home while others single-home, in line with what is observed in reality^11,12,44. We can explore the effect of different multi-homing scenarios on aggregated system performance as well as the experiences of single-homers and multi-homers separately.

• V. Endogenous demand: Unlike most existing approaches, our model accounts explicitly for alternative modes, thereby capturing how ridesourcing propensity depends on travellers’ socio-economic properties, departure time and their trip origin and destination. This allows us to (i) identify which travellers, based on their socio-economic characteristics and trip attributes, are likely to adopt ridesourcing, and (ii) investigate modal split shifts associated with the introduction of ridesourcing services depending on various factors. Hereby, the model provides a more complete picture of the potential effect that ridesourcing provision has on the number of VKT.

The remainder of the paper is organised in the following way. In the ‘Methods’ section, we describe the developed simulation model, including day-to-day and within-day processes associated with multi-homing and single-homing agents in the ridesourcing market. We describe our case study, designed to mimic the city of Amsterdam, and the scenario design of our experiments in the ‘Experimental design’ section. The ‘Results’ section contains a description of the results of our analyses, which are summarised in the ‘Discussion’ section along with their implications for policy makers and future research.

Methods

Assume a ridesourcing market with platforms P = {p₁, …, p_n}, each offering ride-hailing (‘solo’ rides) or ride-pooling in area A. Platforms in P generate revenue by charging a commission on each transaction between travellers and drivers in the market. We assume constant pricing and commissions, both within-day (operational) and day-to-day (tactical). Demand for each platform follows from the mode choice decisions of traveller agents T = {t₁, …, t_b} which make a daily trip within the boundaries of A. The fleet size of ridesourcing platforms depends on the daily work decisions of potential drivers, which we from hereon refer to as job seekers J = {j₁, …, j_l}, who compare the utility derived from driving in the ridesourcing market to the utility of alternative opportunities.

We study the implications of ridesourcing market fragmentation using a simulation model designed to capture multiple day-to-day processes associated with ridesourcing supply and demand, as well as the within-day operations of such markets, as visualised in the conceptual framework in Fig. 2. Specifically, on each day in our day-to-day simulation model of the ridesourcing market the following five subsequent processes take place:

• I. Diffusion of market awareness — a precondition for platform registration — is captured through a peer-to-peer communication process for the aggregated ridesourcing market, i.e. agents learn about the existence of all platforms in P when (first) exposed to information about the ridesourcing market. The awareness diffusion speed depends on the number of unaware individuals as well as the number of market participants.

• II. Agents that are aware of the existence of the market make an occasional platform registration decision, in which they assess the trade off between expected benefits from participating in a platform and long-term costs associated with platform registration (e.g. leasing a vehicle). Here, we also model how they learn about system performance by communicating with agents about recent experiences in the market.

• III. Registered agents then make a daily platform participation decision, in which they compare the expected utility derived from platform participation to the utility of alternatives, i.e. alternative modes for travellers and alternative activities for job seekers. The expected utility derived from using the platform for travellers depends on the expected waiting time, in-vehicle time and ride fare. For job seekers, it depends on the expected financial return.

• IV. In representing the within-day ridesourcing operations following from previously mentioned participation decisions, we capture platforms’ matching of customers to drivers and in case of ride-pooling also to other customers, customers’ ride offer acceptance decisions, as well as drivers’ repositioning behaviour.

• V. Customers and drivers update their expected participation utility for the next day based on their individual experience participating in the ridesourcing market. Day-to-day learning is modelled using an exponential smoothing formulation.

Fig. 2

Conceptual representation of the day-to-day simulation model.

Both traveller agents and job seeker agents in the model are either (inherently) unwilling or willing to multi-home. Specifically, travellers T are subdivided into two subsets: single-homing travellers ${T}^{{\prime} }$, who will only enter in exclusive arrangements with platforms, and multi-homing travellers T^″ who will always register with all platforms in P if they decide to incur market registration costs. Similarly, single-homing job seekers ${J}^{{\prime} }$ will exclusively register with a single platform, whereas multi-homing job seekers J^″ will register with all platforms in P. The probability that travellers and job seekers are open to multi-homing are denoted ρ^trav and ρ^js, respectively.

First, we describe previously mentioned day-to-day processes in the ridesourcing market in more detail for single-homing agents. Then, we elucidate the distinctions in these processes for agents engaged in multi-homing. Finally, we explain how market convergence is established based on double-sided platform participation levels, how we determine the number of replications for statistical significance, and how the computational complexity of the simulation model is kept low.

For the description of the different model components in the remainder of this section, we use set notations for relevant (single-homing) traveller and job seekers subpopulations. These notations are visualised in Fig. 3. First, the populations of single-homing travellers ${T}^{{\prime} }$ and job seekers ${J}^{{\prime} }$ are subdivided into those aware of the ridesourcing market on any given day k — ${({T}^{{\prime} })}_{k}^{{\rm{aware}}}$ and ${({J}^{{\prime} })}_{k}^{{\rm{aware}}}$, respectively — and those not aware — ${({T}^{{\prime} })}_{k}^{{\rm{unaware}}}$ and ${({J}^{{\prime} })}_{k}^{{\rm{unaware}}}$, respectively. Aware agents are further subdivided into individuals registered with platform p (for each p ∈ P) and individuals that are not registered with any platform on day k. Registered agents can be further classified depending on the result of their participation decision on this day. Following from the participation decisions in the day-to-day model, Travellers opting to (exclusively) use a ridesourcing platform p on day k are from hereon referred to as customers ${C}_{pk}^{{\prime} }$, job seekers working (exclusively) for this platform as ${D}_{pk}^{{\prime} }$. ${({T}^{{\prime} })}_{pk}^{{\rm{alt}}}$ denotes travellers registered with p that choose another mode, ${({J}^{{\prime} })}_{pk}^{{\rm{reject}}}$ registered job seekers with p that opt for another activity.

Fig. 3

Tree diagrams visualising set notations. Each branch is related to one of the day-to-day processes in ridesourcing evolution, either awareness diffusion (first branch level in the tree), registration decisions (second level) or participation decisions (third level). a Notations associated with single-homing travellers. b Notations associated with single-homing job seekers.

Awareness diffusion (I)

Insufficient awareness during the initial stages of innovation adoption can impede innovation’s uptake, and for markets with strong network effects where scale directly influences service quality, accounting for awareness diffusion is essential because it allows initial market share differences to amplify through performance disparities, potentially leading to either market failure or monopolistic outcomes. There is generally limited empirical evidence regarding how potential users become aware of innovations, particularly within the context of the ridesourcing market. It is likely influenced by a complex interplay of factors, including peer-to-peer interactions, mass media communication, and platform marketing strategies. Due to the dearth of empirical underpinning for the awareness diffusion process in the ridesourcing market, especially concerning the impact of marketing strategies and global communication sources, we have chosen to employ a model based on peer-to-peer interactions.

Specifically, we adopt the diffusion model proposed by ref.¹ in which the (aggregated) awareness diffusion rate on each side of the market depends on market participation levels. Each day, all travellers T = {t₁, …, t_b} and job seekers J = {j₁, …, j_l} communicate randomly with y^{awareness,trav} and y^awareness,js other individuals, respectively, who may be either aware or unaware of the existence of the market. Communication occurs only within groups: travellers with travellers, and job seekers with job seekers. During an interaction between someone unaware of ridesourcing and a ridesourcing market participant (a driver or customer), we assume a common probability Π of transmitting awareness about the ridesourcing market across travellers and job seekers, as no empirical evidence supports differentiating between the two. Let us denote ${C}_{k}^{{\prime\prime} }$ as the set of multi-homing customers and ${D}_{k}^{{\prime\prime} }$ as the set of multi-homing drivers on day k. Then, the probabilities that unaware travellers and unaware job seekers become aware of ridesourcing market P on this day, respectively, are:

$${\phi }_{tk}^{{\rm{inform,traveller}}}=\frac{\Pi \cdot {y}^{{\rm{awareness,trav}}}\cdot \left(| {C}_{k}^{{\prime\prime} }| +{\sum }_{p\in P}| {C}_{pk}^{{\prime} }| \right)}{b},\,\forall t\in {({T}^{{\prime} })}_{k}^{{\rm{unaware}}}$$

(1)

$${\phi }_{tk}^{{\rm{inform,js}}}=\frac{\Pi \cdot {y}^{{\rm{awareness,js}}}\cdot \left(| {D}_{k}^{{\prime\prime} }| +{\sum }_{p\in P}| {D}_{pk}^{{\prime} }| \right)}{l},\,\forall j\in {({J}^{{\prime} })}_{k}^{{\rm{unaware}}}$$

(2)

The preceding specification of the awareness diffusion model contains the following assumptions:

• Individuals are either entirely unaware or aware of the entire ridesourcing market, i.e. of all or none of the platforms in P.

• Travellers do not receive information about the ridesourcing market’s existence from job seekers, and vice versa.

• Single-homing and multi-homing agents are treated identically in the information diffusion process.

• Ultimately, all travellers and job seekers learn about the ridesourcing market, unless the market reaches an equilibrium in which no travellers or no job seekers participate in the ridesourcing market. This is in line with the widespread familiarity with ridesourcing platforms seen today, as exemplified in the Netherlands⁴⁵.

Platform registration (II)

Since the process of (de-)registering with a platform can be time-consuming and comes with substantial medium- to long-term (financial) commitments, registration decisions have a more tactical nature compared to travellers’ and job seekers’ daily market participation decisions. Therefore, it is assumed that on a given day travellers and job seekers that are aware of the ridesourcing market reevaluate their registration status – being registered or unregistered—with a probability γ. In addition, we assume that they cannot deregister in the first ν days after registering with a platform.

Our model assumes two subsequent decision-making processes in the registration decisions of (single-homing) job seekers. The first one entails the choice between platforms, the second one the choice between being registered with the preferred platform and not being registered at all. Travellers in our model do not make the second decision, following the limited burden associated with demand-side registration, i.e. a few administrative procedures. In other words, we assume that they will always register with one of the platforms in P.

Prior to the registration decision, travellers seek information about waiting time and pooling detours when using ridesourcing platform p, while job seekers seek information about the earnings when driving for this platform. Specifically, we assume that travellers and job seekers are informed about the experiences of y^regist agents participating on their side of the market in platform p on day k − 1, i.e. about their experienced travel time (travellers) and income (job seekers), where each observed experience is given equal weight. We apply exponential smoothing to represent a higher valuation of recent information in comparison to past information, considering possibly on-going evolution of ridesourcing platforms’ participation levels. Particularly, travellers and job seekers assign a weight κ^comm to the average received information signal ${\widetilde{x}}_{tpk}$ and ${\widetilde{x}}_{jpk}$, respectively, based on y^regist interactions, relative to their (personal) previous expectation for relevant indicator ${\widehat{x}}_{tp,k-1}$ and ${\widehat{x}}_{jp,k-1}$. Hence:

$${\widehat{x}}_{tpk}=(1-{\kappa }_{tpk}^{{\rm{comm}}})\cdot {\widehat{x}}_{tp,k-1}+{\kappa }_{tpk}^{{\rm{comm}}}\cdot {\widetilde{x}}_{tpk}$$

(3)

$${\widehat{x}}_{jpk}=(1-{\kappa }_{jpk}^{{\rm{comm}}})\cdot {\widehat{x}}_{jp,k-1}+{\kappa }_{jpk}^{{\rm{comm}}}\cdot {\widetilde{x}}_{jpk}$$

(4)

The assigned weight can vary between registered agents and unregistered agents, considering that the former group can accumulate personal experiences:

$${\kappa }_{tpk}^{{\rm{comm}}}=\left\{\begin{array}{ll}{\kappa }^{{\rm{comm,registered}}} & t\in {({T}^{{\prime} })}_{pk}^{{\rm{registered}}}\\ {\kappa }^{{\rm{comm,unregistered}}} & \,{\rm{otherwise}}\end{array}\right.$$

(5)

$${\kappa }_{jpk}^{{\rm{comm}}}=\left\{\begin{array}{ll}{\kappa }^{{\rm{comm,registered}}} & j\in {({J}^{{\prime} })}_{pk}^{{\rm{registered}}}\\ {\kappa }^{{\rm{comm,unregistered}}} & \,{\rm{otherwise}}\end{array}\right.$$

(6)

Specifically, the indicators travellers learn about are platforms’ waiting time w_tpk, and relative detour factor z_tpk when opting for pooling. Job seekers learn about income i_jpk when spending a day driving for the platform.

When making a registration decision, (single-homing) travellers choose to register with one or none of the platforms in P. The utility derived from registering with platform p depends on the expected utility when travelling with this platform ${U}_{tpk}^{{\rm{travel}}}$, the composition of which is described in the subsection on market participation. We assume that unobserved variables are less prominent in (more tactical) registration decisions compared to daily participation decisions, which we account for by multiplying the travel (participation) utility associated with platform p with parameter θ^trav, taking the value of 1 or more, when determining the utility of being registered with this platform:

$${U}_{tpk}^{{\rm{registered}}}={\theta }^{{\rm{trav}}}\cdot {U}_{tpk}^{{\rm{travel}}}$$

(7)

We apply a Logit model so that the probability of being registered with platform p at the end of day k is formulated as follows:

$${\phi }_{tpk}^{{\rm{registered}}}=\frac{\exp ({U}_{tpk}^{{\rm{registered}}})}{{\sum }_{p\in P}\exp ({U}_{tpk}^{{\rm{registered}}})}$$

(8)

Single-homing job seekers first decide on their preferred platform, assuming they need to register with one, followed by an actual registration decision for this platform. In the first decision, they compare, for all platforms in P, the expected daily surplus s_jpk associated with being registered with platform p over not being registered at all. The definition of the (economic) surplus in our model is taken from ref.⁴⁶. Specifically, the surplus depends on the expected utility ${U}_{jpk}^{{\rm{participate}}}$ derived from driving for the platform and the expected utility ${U}_{j}^{{\rm{alt}}}$ derived from alternative opportunities in the time otherwise spent working. The surplus value accounts for observed and unobserved variables in the participation decision by integration of income sensitivity parameter β^inc:

$${s}_{jpk}=\frac{ln\left(\exp ({U}_{jpk}^{{\rm{participate}}})+\exp ({U}_{j}^{{\rm{alt}}})\right)}{{\beta }^{{\rm{inc}}}}$$

(9)

We refer the reader to the subsection on market participation for the definitions of ${U}_{jpk}^{{\rm{participate}}}$ and ${U}_{j}^{{\rm{alt}}}$.

We apply a Logit model with sensitivity parameter β^reg,platform and error term ε^registration. The utility of being registered with platform p on day k for job seeker j is defined as:

$${U}_{jpk}^{{\rm{registered,platform}}}={\beta }^{{\rm{reg,platform}}}\cdot {s}_{jpk}+{\varepsilon }^{{\rm{registration}}}$$

(10)

The probability that job seeker j prefers platform p ∈ P when being registered in the market on day k is then defined as:

$${\phi }_{jpk}^{{\rm{registered,platform}}}=\frac{\exp ({U}_{jpk}^{{\rm{registered,platform}}})}{{\sum }_{p\in P}\exp ({U}_{jpk}^{{\rm{registered,platform}}})}$$

(11)

We note that ${\phi }_{jpk}^{{\rm{registered,platform}}}$ represents the relative probability between platforms conditional on registration with any platform, rather than the absolute probability that job seeker j is registered with platform p, considering the option to be entirely unregistered from the market. Below, we explain the utilities and probabilities associated with the market registration decision.

First, we assume job seeker j draws platform p^* as their preferred platform for market registration on day k based on probabilities ${\phi }_{jpk}^{{\rm{registered,platform}}},\forall p\in P$. We posit that job seekers incur a daily (non-operational) expense denoted as ϒ when they are registered in the ridesourcing market. With β^reg,market as the monetary sensitivity parameter in the market registration decision, the utility of registering in the ridesourcing market – considering the previous choice for platform p^*—is now denoted as:

$${U}_{jk}^{{\rm{registered,market}}}={\beta }^{{\rm{reg,market}}}\cdot ({s}_{j{p}^{* }k}-\Upsilon )+{\varepsilon }^{{\rm{registration}}}$$

(12)

As for the platform registration model, we assume a logit model specification for the market registration decision. We denote ${\phi }_{jk}^{{\rm{registered,market}}}$ as the probability of being registered in the ridesourcing market on day k for job seeker j making a (de)registration decision at the start of that day. With the utility of the alternative choice — not registering to the market — fixed to 0, this probability is formulated as:

$${\phi }_{jk}^{{\rm{registered,market}}}=\frac{\exp ({U}_{jk}^{{\rm{registered,market}}})}{\exp ({U}_{jk}^{{\rm{registered,market}}})+1}$$

(13)

Job seekers’ sensitivity to monetary gains may be different in platform choice compared to market registration choice. We therefore introduce two separate multipliers θ^js,platform and θ^js,market for converting job seekers’ income sensitivity β^inc in participation choice to the monetary sensitivity parameter in registration choice:

$${\beta }^{{\rm{reg,platform}}}={\theta }^{{\rm{js,platform}}}\cdot {\beta }^{{\rm{inc}}}$$

(14)

$${\beta }^{{\rm{reg,market}}}={\theta }^{{\rm{js,market}}}\cdot {\beta }^{{\rm{inc}}}$$

(15)

Market participation (III)

Every day, travellers ${({T}^{{\prime} })}_{pk}^{{\rm{regist}}}$ registered with ridesourcing platform p decide to request a ride offer using this platform or to opt for another mode of transportation for their daily trip. In making their choices, travellers assess travel time, cost, and mode-specific preferences. Notably, in our model travellers’ value of time may vary across modes, and different time attributes, namely in-vehicle time, waiting time at a stop, and stop access time, may be perceived distinctively. Value of time and mode-specific attributes may also vary among individuals.

Hence, we specify time parameters ${\beta }_{tm}^{{\rm{ivt}}}$, ${\beta }_{tm}^{{\rm{wait}}}$, and ${\beta }_{tm}^{{\rm{access}}}$ to describe a traveller’s perception of in-vehicle time, waiting time and stop access time, respectively. Financial costs associated with the selection of mode m on day k are expressed as f_tmk and allocated a weight of β^cost in the utility function. Preferences associated with modes are accounted for by specifying ASC_tm as the constant of traveller t related to mode m. If public transport is offered, transfers induce an above-and-beyond utility penalty denoted as β^transfer.

Mode attributes and consequently utilities are considered constant from day-to-day for all modes other than ridesourcing. In contrast, in the case of ridesourcing, the (expected) waiting time and in-vehicle time (for pooling) are endogenous variables, while all other variables remain constant.

To address attributes other than time, cost and mode-specific constants in mode choice, a random utility model is employed with error term ε^mode. We define ${\widehat{v}}_{tmk}$ as the (anticipated) time spent on-board a vehicle, a_tmk as the access time required to reach a pick-up location/stop, ${\widehat{w}}_{tmk}$ as the (anticipated) waiting time at a pick-up location/stop, and o_tmk as the number of transfers with mode m on day k. The set of modes is denoted M_k and includes platform p if a traveller is registered with this platform on day k. The utility associated with each mode in M_k for traveller t and the subsequent probability of choosing that particular mode are, respectively, determined as follows:

$$\begin{array}{rcl}{U}_{tmk}^{{\rm{travel}}} & = & {\beta }_{tm}^{{\rm{ivt}}}\cdot {\widehat{v}}_{tmk}+{\beta }_{tm}^{{\rm{access}}}\cdot {a}_{tmk}+{\beta }_{tm}^{{\rm{wait}}}\cdot {\widehat{w}}_{tmk}+{\beta }^{{\rm{transfer}}}\cdot {o}_{tmk}\\ & & +{\beta }^{{\rm{cost}}}\cdot {f}_{tmk}+AS{C}_{tm}+{\varepsilon }^{{\rm{mode}}}\end{array}$$

(16)

$${\phi }_{tmk}^{{\rm{travel}}}=\frac{\exp ({U}_{tmk}^{{\rm{travel}}})}{{\sum }_{m\in {M}_{k}}\exp ({U}_{tmk}^{{\rm{travel}}})}$$

(17)

Every day, registered job seekers decide whether they want to spend their day driving for the platform. We assume that they decide to work when the expected income, denoted as ${\widehat{i}}_{jk}$, surpasses the opportunity costs associated with their working time, represented as r_j. This assumption is in line with the principles of the neoclassical theory of labour supply, as detailed in previous research^47,48,49.

Similar to the previously described registration decision, we utilise a random utility model to account for various factors influencing the participation decision apart from income. These factors include day-to-day fluctuations in job seekers’ reservation wage due to varying activity schedules. We introduce an income sensitivity parameter β^inc and an error term ε^{participation} to encompass income-related and random elements and imperfect knowledge in the decision-making process.

The utility associated with driving, the utility associated with alternative opportunities, and the resulting likelihood that registered job seeker $j\in {({J}^{{\prime} })}_{pk}^{{\rm{registered}}}$ works for platform p on a given day k are, respectively, defined as:

$${U}_{jpk}^{{\rm{participate}}}={\beta }^{{\rm{inc}}}\cdot {\widehat{i}}_{jpk}+{\varepsilon }^{{\rm{participation}}}$$

(18)

$${U}_{j}^{{\rm{alt}}}={\beta }^{{\rm{inc}}}\cdot {r}_{j}+{\varepsilon }^{{\rm{participation}}}$$

(19)

$${\phi }_{jpk}^{{\rm{participate}}}=\frac{\exp ({U}_{jpk}^{{\rm{participate}}})}{\exp ({U}_{jpk}^{{\rm{participate}}})+\exp ({U}_{j}^{{\rm{alt}}})}$$

(20)

Within-day simulation (IV)

The within-day model captures the short-term decision-making of drivers, customers and platforms on day k in a time-based simulation. The goal is to model travel and driving experiences in the market to establish actual experienced attributes for ridesourcing customers and drivers, which likely differ from their expectations in pre-day participation decisions. For customers, these include fare, travel time, and waiting time; for drivers, revenue and cost. The within-day model’s outcomes for the most recent day, combined with historical data, inform travellers’ and job seekers’ decisions about future market registration and participation.

As an outcome of the day-to-day model, input to the within-day simulation are job seekers ${D}_{pk}^{{\prime} }\subset {J}^{{\prime} }$ that decided to work as drivers for platforms p ∈ P. Single-homing drivers have exclusive arrangements with platforms, i.e. ${\bigcap }_{p\in P}{D}_{pk}^{{\prime} }={\rm{\varnothing }}$. Likewise, travellers that seek to use ridesourcing service p on a given day are described by the set of customers ${C}_{pk}^{{\prime} }\subset {T}^{{\prime} }$. Each customer $c\in {C}_{pk}^{{\prime} }$ is described by an origin location ${o}_{c}^{{\rm{req}}}$, destination location ${d}_{c}^{{\rm{req}}}$ and a request time ${t}_{c}^{{\rm{req}}}$. Again, single-homing customers are tied to a single platform, i.e. ${\bigcap }_{p\in P}{C}_{pk}^{{\prime} }={\rm{\varnothing }}$. During the simulation, the goal of each platform is to assign schedules (a sequence of stops) to drivers working for the platform that serve incoming customer requests.

A simulation time step, typically set in seconds or minutes, consists of three main steps: (1) Driver states (e.g. position, on-board customers) are updated according to the currently assigned plan. (2) Incoming customer requests are treated sequentially. Requests are replied by corresponding platforms with an offer consisting of estimated waiting time, travel time and fare, which is used by the customer to decide for (or against) a platform. (3) The platform centrally re-optimises currently assigned driver schedules.

A platform is here assumed to either offer only solo or only pooled rides. In this study, the trip assignment objective for both platforms is to minimise the total driving time for the platform. For a ride-hailing service, this will minimise the time deadheading to pick-up locations and for a ride-pooling service, two customers will share a trip unless the total vehicle time to perform both rides with a single vehicle is longer than two vehicles providing the service. For this study, time constraints are introduced to provide an attractive, yet operationally efficient service for customers. A maximum waiting time of σ^wait and a maximum relative detour/delay time of σ^detour, compared to the direct route travel time, are imposed. The detour/delay time also includes boarding of other passengers, where each boarding process is modelled to last υ seconds.

Offers are created by the platform by inserting the pick-up and drop-off of a customer request into the current schedules of its drivers, and selecting the one with the best change in the above-mentioned criterion. If no feasible option is found, a request is rejected by the platform. From this schedule, expected waiting time and travel time for the customer is extracted. Platforms offering solo rides are operated based on a base fare f^base and a solo km fare f^km. Pooling is offered to travellers at a discount λ on the whole fare. If they receive an offer, single-homing customers will accept this offer, i.e. they do not wait for future offers or (re)consider alternative transport options. After a customer booked the service with one of the platforms, this platform will inform the assigned driver about the new plans. For simplicity, it is assumed that drivers accept all new assignments.

As the insertion procedure usually results in sub-optimal assignments of trip schedules to drivers, a global re-optimisation is triggered and performed by each platform. The algorithm is based on ref.⁵⁰. As this algorithm is not the focus of this study, the reader is referred to ref.⁵¹ for details of its implementation.

Once drivers become idle, i.e. do not have a trip assigned by a platform, they might consider driving to network regions where they expect demand to increase the probability for a new assignment and therefore to increase revenue. It is assumed that these repositioning trips are not suggested by the platform, but rather — similar to platforms like Uber or Lyft — chosen by drivers themselves. Specifically, we assume that idle drivers at the end of each hour consider repositioning to neighbouring zones based on the anticipated (daily) demand (explained in the next subsection) in each of these zones and their current zone. The probability of repositioning to each zone equals the relative share of expected trips in the zone.

After the simulation, drivers evaluate their profit by subtracting driving costs from their revenue, which includes the sum of all fares of customers they served, while considering platform commission rate ψ.

Learning (V)

To capture learning from own experience travelling or working with a platform, we apply a similar exponential smoothing formulation as for learning from other people’s experience, i.e. the process which is described in the subsection on market registration. To be precise, a weight κ^private is assigned to personally experienced system performance indicators on day k relative to previously gathered information up to this day, including information from communicating with others when deciding about platform registration. Hence, if customer $t\in {C}_{pk}^{{\prime} }$ experiences indicator x_tk on day k, their expectation for the value of this indicator ${\widehat{x}}_{t,k+1,p}$ associated with platform p for the next day is defined as:

$${\widehat{x}}_{t,k+1,p}=(1-{\kappa }^{{\rm{private}}})\cdot {\widehat{x}}_{tpk}+{\kappa }^{{\rm{private}}}\cdot {x}_{tpk}$$

(21)

Similarly, if driver $j\in {D}_{pk}^{{\prime} }$ experiences indicator x_jk on day k, their expectation for the value of this indicator ${\widehat{x}}_{j,k+1,p}$ associated with platform p for the next day is defined as:

$${\widehat{x}}_{j,k+1,p}=(1-{\kappa }^{{\rm{private}}})\cdot {\widehat{x}}_{jpk}+{\kappa }^{{\rm{private}}}\cdot {x}_{jpk}$$

(22)

The indicators that customers learn about are waiting time and in-vehicle pooling detour times, whereas drivers learn about income. If a request is denied by the platform, waiting time is perceived to be Γ minutes.

In addition, job seekers also learn about the ridesourcing demand per zone, albeit not from own experience. Our model assumes that at the end of each day all (registered) job seekers are informed about the total ridesourcing demand per zone on that day, e.g. by a transport authority, information that (merely) guides their within-day repositioning decisions. We assume a similar learning process as for the other indicators, i.e. they assign a weight κ^demand to the information provisioned on the last day as opposed to all previously provisioned information.

Multi-homing

In this subsection, we describe how the relevant day-to-day and within-day processes in the ridesourcing market are adapted for multi-homers, i.e. travellers and job seekers that are open to being matched on all platforms in P when they decide to participate in the ridesourcing market on any given day.

The market awareness diffusion process is independent of agents’ willingness to multi-home.

Considering limited demand-side registration costs, multi-homing travellers will choose to be registered with all platforms in P when making a registration decision. Accordingly, multi-homing travellers are not interested in platform-specific indicators and will inquire only about (recent) experiences of multi-homers participating in the ridesourcing market, information that is used to guide future mode choice decisions. We assume that single-homing agents only communicate with registered agents that single-home, specifically about the utility associated with individual platform usage (${U}_{tpk}^{{\rm{participate}}}$, ∀ p ∈ P). Contrary to single-homing travellers, multi-homing travellers also learn about the expected fare when multi-homing, which in a market with a ride-hailing and a ride-pooling provider depends on whether they get assigned to a private or shared ride. Their platform-independent registration decision implies that they experience uncertainty in ride fares, given that solo and pooling providers offer different fares.

The same general principle applies for supplying labour to the ridesourcing market. Multi-homing job seekers do not make a platform decision, and hence are only interested in learning the aggregated market utility ${U}_{jk}^{{\rm{participate}}}$. Single-homing job seekers instead learn about individual platform utilities ${U}_{jpk}^{{\rm{participate}}}$ (∀ p ∈ P). However, contrary to multi-homing travellers, multi-homing job seekers do make a market registration decision, given (possibly substantial) costs ϒ associated with the ability to drive for ridesourcing platforms. These costs are equal for single-homers and multi-homers, i.e. they are only incurred for the first platform.

Similar to the registration decision, multi-homing agents either participate with all platforms or with none of them. To be precise, if multi-homing travellers opt for ridesourcing over other modes of transportation, they request offers on all platforms in P. Essentially, the entire ridesourcing market P is included in the available set of modes M_k, the utility of which depends on platform-independent performance indicators, learnt from other multi-homing agents as well as own experience. Similarly, multi-homing job seekers that choose to work are available to serve requests on all platforms in P. Hence, as opposed to single-homing agents, the participation decisions of multi-homing agents are based on aggregated ridesourcing market utilities ${U}_{jk}^{{\rm{participate}}}$ rather than platform-specific utilities ${U}_{jpk}^{{\rm{participate}}}$, ∀ p ∈ P.

When multi-homing is enabled, small adaptations for drivers and customers in the within-day model are made. In this case, multi-homing drivers ${D}_{k}^{{\prime\prime} }$ are available for work on all platforms in P. Similarly, multi-homing customers ${C}_{k}^{{\prime\prime} }$ request trips from all platforms in P.

For multi-homing drivers, it is assumed that they are available for service for all platforms p ∈ P only when they are idle and looking for new assignments. Once they receive a new assignment from platform $\widetilde{p}$, they log off from all other platforms and are no longer available for driving tasks there until completing assignments from $\widetilde{p}$. During this time, they can get subsequent assignments from $\widetilde{p}$. Only when they become idle again, they log in again to the other platforms. It is additionally assumed that drivers always accept an assigned driving task immediately by any platform. In the model, driver j^* is therefore complemented by a set ${\widetilde{P}}_{{j}^{* }}$ describing the set of currently logged in platforms, which is updated accordingly when a driver receives a new assignment or becomes idle. Before creating an assignment, a platform always checks the logged in drivers.

Multi-homing customers request trips from all platforms in P. The platforms then check feasible solutions, and compute the best solution according to their matching objective — minimising total driving time — and produce an offer based on this solution. If multiple platforms offer the service, the offer (and therefore platform) with the highest utility as given in Eq. (16)– with actual ride offer characteristics and without the error term – is chosen.

In our model, the way multi-homers learn from experience is similar to how single-homers learn from experience. There is again one key distinction: single-homers acquire insights into the service quality of individual platforms, while multi-homers gain knowledge about the collective ridesourcing market.

Convergence

We determine market convergence based on double-sided participation levels. For this purpose, we evaluate the evolution of the number of (single-homing) agents choosing each individual platform as well as the number of multi-homers participating in the market, for both sides of the market. Formally, we define the following two sets of participation indicators, the first set associated with market demand and the second set associated with market supply:

$${G}^{\mathrm{dem}}=\left(\mathop{\cup }\limits_{p\in P}\left\{\left|{({C}^{{\prime} })}_{pk}\right|\right\}\right)\cup \left\{\left|{({C}^{{\prime\prime} })}_{k}\right|\right\}$$

(23)

$${G}^{\sup }=\left(\mathop{\cup }\limits_{p\in P}\left\{\left|{({D}^{{\prime} })}_{pk}\right|\right\}\right)\cup \left\{\left|{({D}^{{\prime\prime} })}_{k}\right|\right\}$$

(24)

In determining convergence, we should neglect random — i.e. non-systematic — day-to-day variations in market participation levels following from random components in peer-to-peer communication and decision-making processes. Formally, we define that the simulation has converged on day k when the absolute day-to-day change in the μ^MA2-day Moving Average (MA) of the μ^MA1-day Moving Average (MA) — nested to further smoothen out random, short-term fluctuations — has been below ω^demand for all demand-side participation indicators g ∈ G^dem and below ω^supply for all supply-side participation indicators $g\in {G}^{\sup }$, each for η days in a row:

$$\begin{array}{l}\left|M{A}_{{\mu }^{{\rm{MA2}}}}{\left(M{A}_{{\mu }^{{\rm{MA1}}}}(g)\right)}_{k-h}-M{A}_{{\mu }^{{\rm{MA2}}}}{\left(M{A}_{{\mu }^{{\rm{MA1}}}}(g)\right)}_{k-h-1}\right|\le {\omega }^{{\rm{demand}}}\\ \forall h\in \{0,\ldots ,\eta \},\forall g\in {G}^{{\rm{dem}}}\end{array}$$

(25)

$$\begin{array}{l}\left|M{A}_{{\mu }^{{\rm{MA2}}}}{\left(M{A}_{{\mu }^{{\rm{MA1}}}}(g)\right)}_{k-h}-M{A}_{{\mu }^{{\rm{MA2}}}}{\left(M{A}_{{\mu }^{{\rm{MA1}}}}(g)\right)}_{k-h-1}\right|\le {\omega }^{{\rm{supply}}}\\ \forall h\in \{0,\ldots ,\eta \},\forall g\in {G}^{\sup }\end{array}$$

(26)

Replications

In light of previously described stochastic processes pertaining to ridesourcing supply and demand, we need to run multiple replications to test and prove the statistical significance of our simulation results. In doing so, we utilise the same indicators that are used to determine convergence. We opt for a method previously applied in simulating monopolist ridesourcing markets^1,52.

This method is based on the sample mean $\overline{g}(q)$ and standard deviation s_g(q) of convergence indicators $g\in {G}^{{\rm{dem}}}\cup {G}^{\sup }$ based on q initial simulation runs. The number of simulation runs that are needed, depending on confidence level 1 − α and allowable error ε^repl of each indicator estimate $\overline{g}$ is determined by:

$$Z(q)=\mathop{\max }\limits_{g\in {G}^{{\rm{dem}}}\cup {G}^{\sup }}{\left(\frac{{s}_{g}(q)\cdot {t}_{m-1,\frac{1-\alpha }{2}}}{{\varepsilon }^{{\rm{repl}}}}\right)}^{2}$$

(27)

in which t_m−1 refers to the Student’s t-distribution with m − 1 degrees of freedom, and the allowable error depends on the absolute value of indicator g and its convergence threshold ζ:

$${\varepsilon }^{{\rm{repl}}}=\left\{\begin{array}{ll}{\varepsilon }^{{\rm{repl,rel}}}\cdot \overline{g}(q) & \overline{g}(q)\ge \zeta \\ {\varepsilon }^{{\rm{repl,rel}}}\cdot \zeta & \,{\rm{otherwise}}\end{array}\right.$$

(28)

Computational complexity

Each day in our simulation model requires modelling numerous decision-making processes involving a substantial population of agents as well as accounting for computationally complex within-day matching between customers and drivers, particularly when ride-pooling is offered. We limit the computational complexity of the simulation model by applying a filter to the traveller population based on their propensity of selecting ridesourcing based on their individual mode choice preferences. Specifically, if traveller agents exhibit a probability lower than the threshold defined by parameter χ even in the ideal conditions — i.e. in a situation where they expect neither waiting time nor in-vehicle delays, while receiving (pooling) discount λ on their fare — then they are subsequently excluded from the initial pool of travellers, i.e. they are assumed to choose another mode on any given day.

Simulation framework

The day-to-day processes associated with ridesourcing supply and demand are implemented in MaaSSim⁵³, and the within-day operational model in FleetPy⁵⁴, both of which are open-source agent-based simulators of mobility-on-demand services programmed in Python. The overarching simulation framework (FleetMaaS) is available here: https://github.com/Arjan-de-R/FleetMaaS.

Experimental set-up

In this part, we outline the set-up of our experiments, which has been designed to mimic the city of Amsterdam, the Netherlands. This pertains to relevant aspects such as the potential ridesourcing market, the underlying road network, ridesourcing operations, and characteristics of alternative modes.

For the travel demand in Amsterdam, we employ a data set generated with the activity-based model Albatross⁵⁵, selecting only trips of 2 km and longer. In terms of the number of trip requests, we sample one-tenth of the total estimated demand in Amsterdam during an 8-h window to limit the computation time of the day-to-day simulation. Similarly, we aim to represent one-tenth of all job seekers residing in Amsterdam. This relative sample size, 10%, aligns with prior research in the domain of agent-based modelling for transportation problems^1,52,56,57. In absolute terms, this sampling yields a total of b = 100,000 travellers and l = 2500 job seekers. In the reference scenario, all of these agents single-home, i.e. ρ^trav = 0% and ρ^js = 0%. In our analysis, travellers with a likelihood of below 5% to select ridesourcing, even under ideal conditions, are assumed to completely disregard ridesourcing, i.e. we set χ to 0.05. This amounts to ~70% of travellers in the reference scenario, aligning with the cumulative share of travellers found in a latent class model to be unlikely to adopt ridesourcing for urban trips in the Netherlands⁴⁵.

Ridesourcing vehicles utilise a road network with spatially heterogeneous yet static travel speeds. Concretely, we assume that drivers operate with a speed of 85% the speed limit. This value has been set so that the average travel speed based on the shortest paths for all origin-destination pairs in Amsterdam approximates the average observed traffic speed in Amsterdam on a working day in reality⁵⁸. We set 30 s as the time needed for pick-ups and drop-offs in ride-hailing (υ = 30). In ride-pooling, each additional stop results in a 10-s delay. Each ride-pooling vehicle has capacity for 4 passengers.

Drivers incur per-kilometre operational costs δ^km of €0.25. Pricing of solo ridesourcing rides is set following Uber’s approach in Amsterdam, omitting surge pricing. This entails charging a base fee f^base of €1.5 and a per-kilometre fee f^km of €1.5. We adopt a generous, guaranteed 33.3% pooling discount to ensure sufficient demand for studying competitive dynamics, significantly higher than typical practice where Uber offers up to 20% when shared with maximal inconvenience⁵⁹. Given that in reality neither of the two ridesourcing providers in Amsterdam offer shared rides, this generous discount could be interpreted as a subsidy scenario that might be needed to make such services viable. Platforms withhold 25% of the fares transferred from travellers to drivers, i.e. ψ = 25%. The daily costs associated with being registered in the ridesourcing market for job seekers is set to €15. Market information about past demand that is communicated to job seekers to guide their repositioning decisions is provided per Gebied (area, majority of which are in the range of 2–10 km²) as established by the municipality of Amsterdam⁶⁰. Platforms adopt a maximum allowed pooling delay σ^detour of 40% the direct in-vehicle time when matching customers to other customers. The time interval between consecutive (re-)assignments is 1 min. Travellers with a ridesourcing request are willing to wait at most 10 min until pick-up, i.e. σ^wait = 10 min.

Beyond ridesourcing, the set of potential travel modes encompasses cycling, private vehicle usage and public transportation, the attributes of which are constant from day to day. The (in-vehicle) travel time with private car is the same as with a ride-hailing (private ride) provider. Access and egress take 5 min each. In addition to per-kilometre operational costs of 0.5 €/km, which are twice as high as those of ridesourcing drivers due to less frequent usage of their cars, private car users are charged a fixed fee of €15 for parking in the city centre — i.e. in areas Centrum-West and Centrum-Oost as specified by the municipality⁶⁰ — and €7.50 elsewhere. Cyclists are assumed to use a private bike, i.e. this travel option is always free of charge. They travel using the same network as cars, yet, at a fixed speed of 15 km/h. Travellers’ travel time and the number of required transfers when travelling with public transport is based on the itinerary leading to the quickest arrival at the destination, queried using OpenTripPlanner for September 19th 2023, based on travellers’ origin, destination and trip request time. Public transport fares are determined based on the (full rate) fares as established by the transport authority of Amsterdam, i.e. a base charge of €1 and an additional €0.20 for every kilometre travelled.

Travellers’ in-vehicle time perceptions, cost perceptions and mode-specific constants are based on a mixed logit model estimated using a data set of stated preference choices⁴⁵ for urban travel behaviour in the Netherlands. In the estimated choice model, in-vehicle time is distributed lognormally and mode-specific constants are distributed normally in the population of travellers. The ride-pooling constant equals the solo (ride-hailing) constant minus a uniformly distributed sharing penalty. We refer to Table 1 for the estimated values of the distributions of in-vehicle time, mode-specific constants and willingness to share.

Table 1 Mode choice parameter distributions

We assume that all travellers perceive waiting time at a stop or pick-up location 2.5 times more negatively and walking time 2 times more negatively than in-vehicle time⁶¹. A minute spent on a bike is perceived 2 times more negatively than a minute spent in a motorised vehicle, accounting for required physical exertion and limited productivity otherwise⁶². Each transfer in public transport is perceived as 5 min of in-vehicle time⁶³ by all travellers. Compared to daily mode choice decisions, we assume that unobserved variables are less dominant in registration decisions by assigning a value of 3 to registration utility multiplier θ^trav.

Job seekers’ reservation wage is distributed lognormally, with a mean of 25 €/h — equal to the average hourly wage in the Netherlands⁶⁴ — and chosen standard deviation so that the resulting Gini coefficient of reservation wage in the lognormal distribution equals 0.35 — close to the Gini coefficient of gross income in the Netherlands⁶⁵. Income sensitivity parameter in participation β^inc is set to 0.05. We set θ^js,market to 20 and θ^js,platform to 100 to represent that job seekers are more income sensitive in tactical registration decisions — particularly in the choice between platforms — than in daily participation decisions. The probability γ that job seekers (re)evaluate their ridesourcing registration status on a given day is set to 15%. They cannot deregister from a platform in the first 5 days after registering, i.e. ν = 5. Daily costs ϒ for being registered in the ridesourcing market add up to €20, based on (short-term) vehicle leasing costs in the Netherlands⁶⁶.

In learning, travellers and job seekers assign a weight of 0.2 to their last private experiences, a weight of 0.2 to the most recent information provided by the platform about zonal demand, a weight of 0.2 to recent information from others based on communication with y^regist = 50 agents when personally registered in the market, and of 0.333 when unregistered. These weights are formally set as κ^private = κ^demand = κ^{comm,registered} = 0.2 and κ^{comm,unregistered} = 0.333. We configure Γ to be 30 min, i.e. we assume that travellers perceive denied service as 30 min of waiting time.

For the assigned parameter values in awareness diffusion, determining convergence—established empirically—and the required number of replications in our experiments, we refer to Table 2.

Table 2 Awareness diffusion (left) and convergence and replication (right) parameters

At the beginning of the simulation, registered job seekers expect to earn the average reservation wage, while informed travellers expect no waiting time and no detour when opting for pooling. Initially, 20% of all agents (job seekers and travellers) are informed. Each initially informed (single-homing) traveller is registered with one of the platforms, while each initially informed job seeker has a 50% probability to be registered with one of the platforms. The initial choice between platforms is random. Each day, job seekers who participate in the market start at a randomly selected location in the network.

Scenarios

In our first set of experiments, we evaluate and compare three duopolistic market structures with two providers at the start of the simulation, differentiated by the service types each platform offers: ride-hailing or ride-pooling. We compare the results to two monopolistic benchmark scenarios.

• Solo-solo: Two platforms each offering a solo (ride-hailing) service (This scenario most closely resembles ridesourcing operations in Amsterdam (Feb. 2025), with two ride-hailing providers (Uber and Bolt) operating in the city, primarily offering private rides—with Bolt exclusively so. Real-world performance metrics for these platforms are lacking. The most recent relevant data comes from a report on Uber’s operations in Amsterdam in 2022⁶⁷. Analysis of the simulated market equilibrium reveals aggregate demand and supply volumes that exceed Uber’s indicators in Amsterdam by a factor of 2–3. These magnitudes are likely consistent with market structure, given that Uber in 2022 operated in a fragmented taxi market alongside Bolt and traditional taxi providers in Amsterdam. Our simulation yields supply-to-demand ratios and driver income patterns that closely parallel Uber’s observed data.).

• Solo-pool: One platform offering a solo service, the other a ride-pooling service.

• Pool-pool: Two platforms each offering a ride-pooling service.

• Solo: Monopolistic platform offering solo (ride-hailing) service (benchmark).

• Pool: Monopolistic platform offering ride-pooling service (benchmark).

The following set of experiments is focused on a market with two service providers each offering ride-hailing (solo-solo). We test the effect of multi-homing behaviour by simultaneously varying the share of travellers and the share of job seekers that are willing to multi-home. For each of the two, we test three values: 0% (only single-homing), 50% (half single-homing, half multi-homing) and 100% (only multi-homing).

The total set of experiments is summarised in Table 3.

Table 3 Design of the two experiments

Results

In this section, we first describe how ridesourcing market outcomes are dependent on the number of service providers and their offered service types (private or pooled rides), including studying market evolution towards the eventual equilibrium state. We evaluate performance indicators associated with different stakeholders, explore which users are attracted to the market based on heterogenoeus travel time perceptions and trip distances, and present associated modal shifts. Then, we demonstrate the market impact of multi-homing behaviour by travellers and job seekers, including exploring the added value of multi-homing for participants on each market side.

Market structure & service types

Figure 4 shows that the market may develop towards a winner-takes-all market equilibrium when two platforms offer a solo service (solo-solo scenario). Figure 5 provides an explanation for this development, highlighting the evolution of key performance indicators for five different replications. In early phases of market evolution, both demand (Fig. 5a) and supply (Fig. 5c) are subject to (purely) random day-to-day variations resulting in (random) differences in the average customer waiting time (Fig. 5b) and driver income (Fig. 5d) between platforms. This kick-starts a reinforcing feedback loop that leads travellers and drivers to gradually switch to the initially more lucky (and consequently larger) platform, which previously offered lower waiting times and higher earnings. Figure 5 illustrates that the time required to reach a winner-takes-all outcome varies substantially between replications, influenced by the randomness in participation decisions during the initial days. Figure 4 demonstrates that the resulting (winner-takes-all) equilibrium in the solo-solo market is similar to the equilibrium if only one platform had initially entered the market (solo).

Fig. 4

Evolution of five key ridesourcing market indicators based on a single replication of the experiment for each of the market types: demand for ridesourcing, the average time from requesting a trip to being picked up by a driver, the average ride-pooling detour time relative to travellers’ average shortest-path travel time, ridesourcing fleet size, and the average income of a ridesourcing driver per day. A market with one initial service provider converges to equilibrium within 200 days, whereas markets with two initial providers take more time to converge. Specifically, when both providers offer ride-pooling, convergence takes the longest — nearly 400 days. While this figure shows the evolution of performance indicators for only one replication of each scenario, we observe similar patterns in other replications, even though the speed of convergence varies. Figure 5 illustrates the evolution of the ridesourcing market across different replications of the solo-solo market scenario.

Fig. 5

Evolution of five key ridesourcing market indicators (first 200 days) in the solo-solo market for multiple replications of the experiment. Based on a scenario where travellers/job seekers communicate with y^regist = 50 others about travel time/income; similar but more gradual developments are observed when they communicate with fewer others. a Demand for ridesourcing. b The average time from requesting a trip to being picked up by a driver. c Ridesourcing fleet size. d The average income of a ridesourcing driver per day.

In a market in which one platform offers a solo service and the other a pooling service (solo-pool), both platforms can co-exist. We observe that the solo platform attracts more demand and particularly more supply than the ride-pooling platform. With more active drivers per trip request, travellers opting for the solo provider experience a lower waiting time than users of the ride-pooling platform. For instance, nearly all solo users are picked up within 5 min of requesting a ride, whereas a substantial number of ride-pooling users experience a waiting time of over 5 min (Fig. 6a). In addition, the majority of ride-pooling users faces an additional delay due to detouring to pick-up other passengers, with a maximum of 9 min (Fig. 6b). Yet, ~4000 travellers prefer ride-pooling over ride-hailing due to the lower pooling fares. Notably, drivers experience (roughly) the same earnings on both platforms, the distribution of which is shown in Fig. 6c for a random day in the equilibrium state. Selecting the platform that offers solo rides results in a higher revenue per served traveller; however, also leads to elevated operational costs per served traveller. Additionally, drivers face more idle time when working for the solo platform, a consequence of heightened supply-side competition within this platform.

Fig. 6

Distribution of experienced platform participation indicators in the solo-pool market, based on a random day in equilibrium and on a single replication of the experiment. a Waiting (pick-up) time. b In-vehicle time. c Daily driver income.

The market with two ride-pooling providers (pool-pool) evolves towards an equilibrium with two approximately equally large platforms. A likely contributing factor for why a winner-takes-all scenario does not occur in such a market in our experiments, as opposed to a solo-solo market, is that pooling discounts are offered ex-ante, i.e. discounts are independent of actual sharing. Hereby, travellers will opt for the platform with the fewest other users to limit the chance of actually sharing their trip with other travellers, providing them with a (more) direct trip for the same fare. This negative network effect in ride-pooling has been described as the extra-detour effect by ref.¹⁴. In this case, this effect prevails over two positive network effects in ride-pooling: (i) the so-called better-matching network effect— more compatible trips result in less detouring—which generally occurs under already dense demand, whereas ride-pooling in our experiments has a limited market share, and (ii) a network effect resembling the Mohring effect in public transport—drivers choosing the platform with most demand to maximise their productivity.

When considering the (demand-side) market share of ridesourcing markets depending on which services are offered (Fig. 7), we find that the largest market share (over 10%) is attained when one platform offers a ride-hailing service and the other a ride-pooling service. The ride-hailing platform in this market caters for time-sensitive users and the ride-pooling platform for less time-sensitive users, typically with relatively long trips (Fig. 8). If only ride-pooling is offered, either by a single provider or two providers, the market share is still close to 10%, as time-sensitive users may prefer ride-pooling over other modes when no private rides are offered in the market. We find that in all scenarios in which ride-pooling is provided by at least one platform, 2.3–2.4% of all travellers, a relatively large share of ridesourcing users compared to other scenarios, would have otherwise opted for public transport. The market share of ridesourcing is most limited when only the solo service is provided, as some cost-sensitive users prefer using public transport considering its lower fares. Yet, still over 9% of travellers will choose ridesourcing in such a scenario.

Fig. 7

Market share of ridesourcing in the market equilibrium depending on the number of (initial) service providers and their service types, including what modes would have been chosen if ridesourcing had not been offered.

Fig. 8

Relative market share of ride-hailing (solo) and ride-pooling (pool) for different user segments (deciles). a Travellers’ value of time. b The distance of their trip.

Ride-pooling is anticipated to provide a more efficient service in terms of the vehicle kilometres needed to serve a single user compared to ride-hailing. Figure 9 shows for different market types the number of ridesourcing vehicle kilometres divided by the sum of the shortest path distances between users’ origins and destinations in the market equilibrium. A value of less than 1 essentially implies that the ridesourcing system is more efficient than a system in which everybody uses a private car to travel between their origins and destinations. We observe, however, that in all scenarios, independent of the number of (initial) service providers and service types that are offered, the number of vehicle kilometres per effective passenger kilometre—defined as the sum of vehicle kilometres divided by the sum of shortest path distances of all trips served in the ridesourcing market—is at least 1. It implies that ridesourcing in our experiments is never more efficient in terms of the total vehicle distance than private car usage. The ridesourcing market is least inefficient when ride-pooling is offered by a single service provider (pool). In such a scenario, multiple passengers share a vehicle for a substantial portion of all vehicle kilometres. Yet, high-occupancy sharing is rare given the fairly limited market share of the ride-pooling provider. At the same time, a substantial number of empty vehicle kilometres are generated due to repositioning and driving to users’ pick-up locations. When the ride-pooling market is subdivided over two platforms (pool-pool), less efficient matches are produced, and hence, the total VKT to serve similar demand is 6.4% higher than in a market with one ride-pooling provider.

Fig. 9

Total VKT of ridesourcing vehicles divided by the sum of the shortest path distances between ridesourcing users’ origins and destinations.

When one platform offers a ride-hailing service and the other a ride-pooling service (solo-pool), substantially less sharing takes place. Users opting for the ride-pooling platform for instance never share their vehicle with more than one co-rider at a time. At the same time, more repositioning takes place as more drivers are attracted to the ridesourcing market, relative to ridesourcing demand, inducing higher driver idle time. In such a market, ~1.20 vehicle kilometres are generated for each effective kilometre on the shortest path between users’ origins and destinations. A ridesourcing market without ride-pooling (solo or solo-solo) is least beneficial from a vehicle kilometre standpoint as each effective passenger kilometre induces 1.29 vehicle kilometres. Not only do drivers never serve multiple passengers simultaneously, they also spend significant time repositioning in anticipation of new requests. The reason is that relatively many drivers are attracted by the higher fares of the solo service compared to the pooling service, resulting in substantial driver idle time, which induces repositioning.

Multi-homing

Insofar, we assumed that all agents (travellers and job seekers) enter in exclusive arrangements with platforms. Our model allows to test alternative scenarios in which some or all travellers and/or job seekers are open to multi-homing, i.e. will register either with all or none of the platforms. In this subsection, we do so for a market with two solo providers (solo-solo). First, we examine a scenario in which half of travellers and half of job seekers multi-home.

In Fig. 10 we present key performance indicators differentiating single-homing and multi-homing agents. Figure 10a shows that nearly 5000 multi-homing travellers—10% of the total—request a ride in the ridesourcing market (using both platforms). Of the single-homing travellers, a small majority requests a ride on the platform that offers the lowest waiting time (Fig. 10b), whereas a smaller share of travellers requests with the competitor, following past personal luck with the platform or positive information signals from others. On average, travellers open to multi-homing are marginally more likely to request in the ridesourcing market than travellers unwilling to engage in multi-homing. We observe a similar pattern on the supply-side (Fig. 10c), i.e. one platform attracts a higher number of single-homing job seekers than its competitor. This stems from the difference in earnings observed between the two platforms (Fig. 10d). As with travellers, job seekers who are willing to multi-home are more likely to participate in the market than those who are not. This difference is more pronounced among job seekers than among travellers.

Fig. 10

Market participation volumes and experiences, differentiating between agents opting exclusively for the leading platform, agents opting exclusively for the competitor (smaller platform), and agents opting for both platforms (multi-homing) in a scenario in which 50% of job seekers and 50% of travellers are open to multi-homing. a The number of travellers requesting trips in the market. b The average waiting time (pick-up time). c The number of job seekers driving in the ridesourcing market. d The average driver income.

Figure 10 also provides insight into the added value of multi-homing for both travellers and job seekers (explaining previous described differences in market participation between single-homing and multi-homing agents). For travellers, it increases their chances of being matched to nearby drivers, reducing their average experienced pick-up time to ~78 s, compared to 94 using only the leading platform and 111 requesting only on the competitor platform (Fig. 10b). For drivers, it increases their chances of being assigned to nearby trip requests, reducing their idle time. It results in an average income of €120.97 per day, compared to €106.90 for drivers working only for the leader platform and €102.34 for drivers working only for the competitor.

Our results highlight that in the scenario in which half of travellers and half of job seekers prefer to multi-home each platform manages to attract both multi-homing travellers/job seekers and single-homing travellers/job seekers, even though one platform offers a lower waiting time and higher earnings than the other. We observe a similar market equilibrium when half of travellers multi-home but none of the job seekers do (Fig. 11a, d). When half of job seekers multi-home but none of the travellers do, all single-homing job seekers will opt for the same platform, as this platform offers substantially higher earnings. On the smaller platform, they compete for too limited demand with multi-homers available on both platforms. It illustrates that a general lack of willingness to multi-home may result in a more skewed market equilibrium in terms of platforms’ market shares.

Fig. 11

Key ridesourcing performance indicators across different two-sided multi-homing scenarios. a Leading platform’s demand-side market share (trip requests). b Total unique trip requests. c Average pickup time. d Leading platform’s supply-side market share (drivers). e Total unique drivers. f Average daily driver income. g Vehicle distance efficiency: total distance in km / effective passenger-km, where effective passenger-km refers to the sum of shortest path distances between users’ origins and destinations. h Pickup distance ratio: pickup distance in km / effective passenger-km. i Repositioning distance ratio: repositioning distance in km / effective passenger-km.

We observe that when all travellers multi-home, all job seekers multi-home, or both, the market evolves towards an equilibrium with two equally large platforms. In such a scenario, either demand or supply (or both) is guaranteed to be equal due to one side of the market’s multi-homing behaviour, hence, platform choice becomes irrelevant for single-homing agents on the other side of the market. Hence, single-homers are equally likely to opt for either platform.

Our results show that as multi-homing counteracts market fragmentation costs in markets with more than one service provider, an increase in the willingness to multi-home in the population results in higher total demand for ridesourcing (Fig. 11b), associated with a decrease in the average request pick-up time (Fig. 11c). Similarly, multi-homing can result in higher supply (Fig. 11e) following an increase in driver earnings (Fig. 11f). Notably, market supply and demand are (slightly) higher in the scenario in which all agents multi-home and both platforms are equally large than in the market equilibrium in which only one platform remains as the sole provider—the scenario in which no agent is willing to multi-home—even though the ridesourcing market is not confronted with market fragmentation costs in either case. This can be explained by the fact that in the multi-homing scenario, travellers always choose between two offers, opting for the one that offers them the highest utility, i.e. minimal pick-up time when no ride-pooling is offered. The ride offer can differ between platforms as drivers that are assigned to serve a request on a platform are assumed to temporarily log off from the other platform. It implies that they can be scheduled to serve a consecutive request on the first platform but not on the second. Apparently, in our experiments a system in which travellers choose between offers results in a better system performance than a system in which platforms decide about the offer, which in this case is based on a minimisation of the total driving time in the system, excluding driver repositioning. Figure 11g shows vehicle distance efficiency across different multi-homing scenarios, measured as total vehicle kilometres divided by effective passenger distance, the latter defined as the sum of shortest path distances between users’ origins and destinations. While differences between scenarios are relatively modest, the most efficient scenario occurs when all agents multi-home, while asymmetric single-homing scenarios—where all participants on one side single-home and half on the other side single-home—prove least efficient. As Fig. 11h demonstrates, this efficiency gap stems from market fragmentation into two platforms with unequal market shares, resulting in relatively long pickup distances on the smaller platform. Market fragmentation costs—increased pick-up distances—are absent when no participants multi-home (winner-takes-all) or when all participants on at least one side multi-home (enabling optimal matching across platforms). Finally, when drivers cannot multi-home, fewer travellers end up requesting rides (Fig. 11b), leading to increased driver idle time and higher repositioning distances (Fig. 11i).

Discussion

Our experiments demonstrate that network effects in the provision of ride-hailing (solo rides only) facilitate winner-takes-all markets. Random initial differences in platforms’ two-sided participation levels translate into structural differences as participation with the larger platform yields shorter waiting times and higher earnings. We observe that a winner-takes-all scenario does not occur when at least one of the service providers opts for pooled rides. When both platforms offer ride-pooling, ex-ante pricing discounts incentivise travellers to opt for the platform with more limited demand to minimise detours from pooling, even though drivers prefer the platform with most trip requests. Apparently, negative network effects in ride-pooling, namely extra detours and increased competition for matches, may outweigh positive network effects of induced supply and better matches. Based on our findings, two platforms can also co-exist when one offers ride-hailing and the other ride-pooling. Both services cater to different travellers, not only based on their sensitivity to time—as shown by our analysis and previously by a latent class analysis of urban travel behaviour in the Netherlands⁴⁵—but also on the distance of their trip. In our experiments, the solo provider attracts more users and particularly more drivers than the ride-pooling provider. Drivers face the same earnings on both platforms, with shorter idle time on the ride-pooling platform and higher revenue per served request on the ride-hailing platform.

Our results also provide insights into the costs of market fragmentation in ride-pooling markets. Due to less efficient matches, each effective passenger kilometre requires 6.4% more vehicle kilometres in a duopolistic ride-pooling market compared to a monopolistic one. The effect of market fragmentation on travel time, driver earnings and platform revenue is found to be limited.

Markets where at least one platform offers ride-pooling are more efficient in terms of vehicle distance than pure ride-hailing markets, not only because passengers share rides but also due to reduced (empty-vehicle) repositioning. Since ride-pooling platforms attract fewer drivers than ride-hailing platforms, their drivers experience less idle time, thereby lowering their need for repositioning.

Furthermore, our study sheds light on potential modal shift patterns following the introduction of ridesourcing, indicating that markets in which ride-pooling is offered attract relatively many, generally cost-sensitive, public transport users relative to markets without ride-pooling. This may at least partially negate the benefits of ride-pooling when it comes to serving passengers with minimal vehicle VKT. At the same time, our results demonstrate that there is a large overlap in the target group of ride-hailing and ride-pooling platforms, i.e. the total market share of ridesourcing is only marginally larger when both ride-hailing and ride-pooling are offered compared to markets in which one of the two is offered.

Our experiments highlight that multi-homing can prevent the emergence of a winner-takes-all platform in markets with two initial ride-hailing providers. When either all travellers, job seekers, or both, multi-home, both platforms reach approximately equal sizes in the market equilibrium. An equilibrium state with one larger and one smaller platform can also emerge. This occurs when some travellers and/or some job seekers (but not all) multi-home. In that case, there may be a discrepancy in earnings and waiting time between two platforms, with the majority or all single-homing travellers and job seekers choosing the larger (better) platform, and multi-homers participating on both platforms. Our results also provide insights into the benefit derived from multi-homing. In a market in which half of travellers and half of job seekers multi-home, multi-homing drivers earn ~€14 per day more than drivers working solely for the larger platform and ~€18 more than drivers working solely for the smaller platform. Travellers are also better off multi-homing. Their average waiting time is 16 s shorter than the waiting time of travellers requesting only with the larger platform, and approximately half a minute shorter than travellers requesting only with the smaller platform.

While ride-pooling efficiency has been found previously to depend critically on scale, our research shows this problem is likely compounded by market fragmentation resulting from negative network effects (longer detours) under limited demand. The effect of alternative modes is crucial: ride-pooling is more interchangeable with public transport and cycling than with private car usage, preventing scaling in contexts with quality infrastructure while attracting users primarily from already efficient modes. Additionally, ride-pooling competes with private ride-hailing services, which draw significant demand away from pooled options.

These findings suggest transport authorities should consider limiting market entry to prevent counterproductive fragmentation, or alternatively, encourage multi-homing behaviour to mitigate fragmentation costs. Policies should also account for the competitive dynamics between ride-pooling and ride-hailing services. More fundamentally, in contexts with high-quality public transport and cycling infrastructure, policymakers may need to question whether introducing ride-pooling services is beneficial at all, given they may operate inefficiently while drawing substantial demand from more sustainable modes under those conditions.

While this study has explored several aspects of ridesourcing market evolution, many areas remain under-investigated and warrant further research. For instance, the evolution of ridesourcing markets can be studied in alternative contexts. This includes examining markets with more than two initial service providers and those where individual platforms simultaneously offer private and shared rides. Given that service differentiation between platforms appears to enable coexistence, future research could explore whether platforms with different matching algorithms and service types—including variations in pick-up/drop-off flexibility—can serve distinct user segments or if superior algorithms further contribute to competitive dominance. Other factors of which the effect can be tested using our model include the properties of alternative modes, travel demand characteristics (including trip density and travellers’ preferences), and labour market conditions. Such studies would help to determine the conditions under which ridesourcing platforms are likely to coexist, a single platform is likely to dominate, or all platforms may cease to exist, possibly due to the tragedy of the commons in ridesourcing provision. While the current study assumed static market conditions, our model can also be used to investigate how ridesourcing markets respond to changing contexts, such as a sudden drop in demand like the one witnessed during the COVID-19 pandemic.

In addition, future research may focus on evaluating more complex (possibly dynamic) platform pricing strategies—i.e. platforms strategically setting fares of ride-hailing and ride-pooling (with pooling discounts determined ex-ante or ex-post based on the inconvenience of sharing) as well as platform commission—to gain better insights into the implications of platform competition, in addition to platform co-existence as studied in this work. This includes studying the effect of (possibly two-sided) loyalty programs. At the same time, future research may explore in more detail cooperation strategies to minimise market fragmentation costs among platforms, such as the introduction of a broker platform³⁴.

Finally, there is a significant gap in understanding several day-to-day processes in the ridesourcing market, presenting a crucial area for future research, particularly regarding information diffusion. Given the limited empirical evidence, we used simplified models as a starting point for model development, with the intention of incorporating more complex factors as more data becomes available. Market awareness could, for instance, be influenced by market utility or participation levels. Additionally, there could be platform-specific awareness not accounted for here. Furthermore, the model could be extended to include endogenous multi-homing, where travellers and job seekers decide to multi-home based on a comparison of the benefits and costs associated with multi-homing. Addressing these research gaps will provide deeper insights into the dynamics of ridesourcing markets, which can support effective policies for improving driver income, reducing user travel time, increasing platform revenue, and decreasing overall traffic levels.