Study on the interactive evolution mechanism of residents’ energy use behavior in shared living spaces

Abstract

Guiding residents of shared living spaces to implement energy-saving behaviors can help improve building energy efficiency and promote the realization of the Carbon Peaking and Carbon Neutrality Goals. Since there are different subjects with different energy-use behaviors in shared living spaces, exploring how these heterogeneous subjects interact with each other is the key to guiding the energy-saving behaviors of residents in shared living spaces. Therefore, based on the evolutionary game theory, this study quantifies the utility of heterogeneous subjects under different combinations of strategies from five dimensions: social, environmental, economic and comfort needs, and effort, and constructs a mechanism model of the interaction and evolution of energy-use behaviors of heterogeneous subjects in shared living spaces. Subsequently, the student dormitory is taken as an example, data are obtained through questionnaires and matlab is used to analyze the interactive evolution process of heterogeneous subjects’ energy-use behaviors, findings demonstrate that enhancing the likelihood of heterogeneous individuals adopting energy-saving strategies can be achieved through various means. When the time spent with roommates is 0–1 year, effective approaches encompass enhancing interpersonal relationships, diminishing comfort levels, heightening attention to energy-related concerns, escalating the cost associated with energy consumption, mitigating the effort required for habituating energy-use changes, bolstering perceived behavioral control, and augmenting perceived behavioral control. These efforts serve to render energy-use behaviors of heterogeneous subjects more efficacious. Furthermore, when the time spent with roommates is 1–2 years, adjustments such as judiciously reducing comfort levels or elevating the costs associated with energy consumption can be implemented. Finally, when the time spent with roommates is 2–3 years, interventions involve fostering collective consensus on energy conservation, diminishing comfort levels, or reinforcing individual norms.

Introduction

The increase in greenhouse gas emissions has exacerbated the process of global warming, and to reduce its emissions, China has set the goal of “achieving carbon peak by 2030 and carbon neutrality by 2060”. Currently, carbon dioxide emissions from energy consumption account for two-thirds of global emissions¹. In 2018, building energy consumption accounted for 36% of global end-use energy consumption, and CO₂ emissions from building energy consumption accounted for 39% of total global energy-related CO₂ emissions, making buildings the world’s top energy consumer and CO₂ emitter². Therefore, improving the energy efficiency of buildings will help China to achieve its energy-saving and emission-reduction goals successfully.

The energy consumption generated by shared living spaces is an important part of building energy consumption. A shared living space is a building space where a specific group of people live and reside together³. The building energy consumption generated by this particular building space accounts for 38% of the total building energy consumption and 42% of the total building carbon dioxide emissions², so realizing the energy saving and emission reduction of shared living space is crucial for building energy saving and emission reduction. The behavior of building users is often the main reason for the inefficiency of building technology solutions and the failure of energy saving^4,5,6,7, and therefore relying on technology alone does not ensure the achievement of the goal of reducing the energy consumption of buildings, human behavior should be considered at the same time⁸. Moreover, building energy consumption can be reduced continuously and effectively through human energy-saving behaviors⁹. Therefore, guiding the residents of shared living spaces to implement energy-saving behaviors is an important way to achieve energy-saving and emission reduction in buildings.

Fully understanding the energy use behavior of residents in shared living spaces is the first and very important step to achieve energy conservation. However, shared living space is significantly different from other building spaces, mainly manifested in the fact that people need to share living space and resources, and jointly bear the resulting costs¹⁰, have equal rights to use and decide on the use of public space and resources¹¹, and will form stable and close interpersonal relationships¹², which makes people’s energy-using behaviors in shared living space very different from their energy-using behaviors in other building spaces, specifically:

First of all, there are subjects with different energy-using behaviors in the shared living space¹³. The reason is that when people have equal rights to use and decide on the use of public energy-using equipment, to a large extent, it will prompt people to use energy-using equipment according to their characteristics of energy-using behavior, thus forming subjects with different energy-using behaviors. These subjects with different energy-using behaviors are in the same building space, so they will inevitably influence each other’s energy-using behaviors, which ultimately affects the energy consumption of the whole building space.

Secondly, the mutual influence of the energy use behavior of residents in shared living spaces is a complex process. The reason for this is that the formation of stable and close interpersonal relationships and the characteristics of sharing energy-using equipment and energy-using costs with others make energy users in shared living spaces not exist in isolation, but in a group environment¹⁴. Therefore, the energy use behaviors of residents in shared living spaces are not only influenced by some individual-level factors, but also more likely to be influenced by group factors, such as group norms, group identity, and group interpersonal relationships¹⁵, which interact with each other to shape the strategic choices of residents in shared living spaces in terms of energy use.

Again, the mutual influence process of heterogeneous subjects’ energy-using behaviors in the shared living space does not reach a stable state instantly but gradually reaches a certain stable state with time. The reason is that the formation of stable and close interpersonal relationships is a process¹⁶, that makes it necessary for residents in shared living spaces to adopt appropriate energy-using behaviors according to the development process of interpersonal relationships. Specifically, people in a shared living space cannot anticipate which energy-using behaviors other individuals will choose at the beginning, and it is almost impossible for them to choose the energy-using behaviors that are the most beneficial to all of them at the beginning, but they will gradually adjust and improve their energy-using behaviors by learning or imitating the energy-using behaviors of other individuals¹⁷, and then gradually reach a certain stable state. It is worth noting that this stable state is not static, and when some external conditions change, the original stable state will also change¹⁸. Therefore, only by clarifying how the energy-using behaviors of the residents in shared living spaces interact with each other can corresponding strategies be adopted in a targeted manner, so that the energy-using behaviors of the building users in shared living spaces can be changed to a more energy-saving direction, and the energy consumption of the whole shared living space can be reduced.

Existing studies have designed the decision function of energy use behavior in the following aspects when exploring the interaction mechanism of the subject’s energy use behavior: ①Comfort utility, which mainly refers to people’s thermal comfort¹⁹, visual comfort, sound comfort, etc., of their surroundings²⁰; ② Perceived psychological utility, which mainly involves parameters related to energy conservation awareness²¹, energy conservation attitudes, perceived behavioral control²², value; ③ economic utility, which mainly involves parameters related to the cost of energy use, such as the amount of energy consumed²³ and the price of energy²⁴; ④ social influence utility, which mainly refers to the pressure from family and coworkers²⁵, the influence of peers and elders²⁶, and social norms/subjective norms²⁷. Regarding the design of decision rules for energy-using behaviors, in general, people choose to implement the behavior that maximizes the utility of one or more of the above dimensions. The specific energy-use scenarios involved in the research on the interaction mechanism of the subject’s energy-use behavior mainly include: office buildings and residential buildings²⁸, whose scale can be expanded from a single room to a group of buildings²⁹. Overall, the above studies provide ideas for this paper to explore the interaction evolution mechanism of the subject’s energy use behavior in shared living spaces.

More importantly, inter-individual emotional ties or relationships and the expectation of gaining the respect of others also have an impact on the energy-using behaviors of shared living space residents¹⁵. However, when exploring the interaction mechanism of the subject’s energy-using behavior, existing studies have seldom considered the social utility gained by the subject when choosing the corresponding strategy. Meanwhile, it takes a certain time for the subject’s energy use behavior to evolve from the initial state to the stable state in the shared living space, and the process will be accompanied by the change of the total utility when the subject chooses the corresponding strategy, which is seldom involved in the existing research. Therefore, by exploring the interactive evolution mechanism of energy use behavior of residents in shared living spaces, this paper can not only make up for the shortcomings of the existing research but also reveal how the energy use behavior of residents in shared living spaces interacts with each other, which is of great significance for realizing energy saving and emission reduction in buildings.

Theoretical foundation and model construction

Theoretical foundations

Basic overview of evolutionary game theory

The basic idea of Evolutionary Game Theory³⁰ is that there will be more than one (N ≥ 2) participants in the game system (i.e., the group), and under the assumption of finite rationality, people can not anticipate what kind of strategy will be chosen by the participants at the beginning of the game, and the participants of the game can not choose the optimal strategy in the first time of the game. But they can learn or imitate the behavior of other participants³¹, in the repeated process of the game constantly adjust and improve their own choice of strategy, and finally make the game system gradually stabilized in a certain equilibrium strategy, of course, this stabilization result is not static, when certain conditions change, the original homeostasis will also change.

Due to the research objectives of this study aligning with evolutionary game theory, it aims to explore how different energy consumption behaviors of subjects in university dormitories interact over time, and to explain the stable states that energy consumption behaviors will reach under various conditions, as well as the process of reaching a certain state. This is also a problem addressed by evolutionary game theory. Therefore, this paper uses evolutionary game theory to study the interactive evolution mechanism of energy consumption behaviors in university dormitories.

Deficiencies

Nevertheless, when evolutionary game theory or its extension theory is used to study the mechanism of the interactive evolution of heterogeneous subjects’ energy-using behaviors in shared living spaces, the following shortcomings can be found: ① in shared living spaces, since the key influencing factors affecting different subjects’ strategy choices and the intensity of their effects change with the prolongation of the interaction time of the subjects, the utility perceptions of the subjects on a certain strategy will also change with the prolongation of the interaction time of the subjects under the effect of the key influencing factors, but the evolutionary game theory considers that the utility obtained by the subject when choosing the corresponding strategy is unchanging; ② In the shared living space, different subjects in the selection of the corresponding strategy, in addition to considering the needs of comfort, economy, environmental protection, and so on, will also take into account the social needs, but the theory of the evolutionary game does not pay attention to the subject’s social needs on the impact of the subject’s strategy choice.

Construction of theoretical models

Research boundary limitations

Limit 1: In the shared living space, people are finite and rational.

Limit 2: In a shared living space, there are two different types of subjects: A represents the saving type and B represents the wasting type, with each group’s set of energy use behaviors consisting of S1 = conservation and S2 = wastefulness.

Limit 3: Assume that in the initial state, the probability that A chooses the “frugal” strategy is x, and the probability that A chooses the “wasteful” strategy is 1-x; the probability that B chooses the “frugal” strategy is y, and the probability that B chooses the “wasteful” strategy is 1-y. In addition, both x and y are functions of time t.

Limit 4: It is assumed that when both members A and B choose strategies ${S}_{1}$, the utility function of member A is ${U}_{A1}$, and the utility function of member B is ${U}_{B1}$; when both members A and B choose strategies ${S}_{2}$, the utility function of member A is ${U}_{A2}$, and the utility function of member B is ${U}_{B2}$; when member A chooses a strategy ${S}_{1}$, and member B chooses a strategy ${S}_{2}$, the utility function of member A is ${\text{U}}_{\text{A}1}{\prime}$, and the utility function of member B is ${\text{U}}_{\text{B}2}{\prime}$; when member A chooses a strategy ${S}_{2}$, and member B chooses a strategy ${S}_{1}$, the utility function of member A is ${\text{U}}_{\text{A}2}{\prime}$, and the utility function of member B is ${\text{U}}_{\text{B}1}{\prime}$.

where ${\text{U}}_{\text{A}1}, {\text{U}}_{\text{B}1}$, ${\text{U}}_{\text{A}2}, {\text{U}}_{\text{B}2}{,\text{ U}}_{\text{A}1}{\prime}, {\text{U}}_{\text{B}2}{\prime}$, ${\text{U}}_{\text{A}2}{\prime}\text{ and }{\text{U}}_{\text{B}1}{\prime}$ are all functions of the degree to which social, environmental, comfort and economic needs are satisfied and the degree of effort required to choose a particular strategy. Among these, social needs include maintaining good interpersonal relationships and gaining group recognition; environmental protection needs mainly involve adhering to individual environmental protection standards and ethical norms, as well as paying attention to energy issues; comfort needs primarily focus on meeting personal requirements for indoor environmental comfort; economic needs mainly refer to minimizing energy costs as much as possible; the effort required to choose a certain strategy mainly involves making changes to one’s existing energy usage habits as much as possible.

Limit 5: In a shared living space, the strength of the effects of the factors influencing which energy-using behaviors are chosen by the two players of the game varies over time, i.e., the coefficients ${a}_{A1i}$, ${a}_{A2i}$, ${a}_{B1i}$, ${a}_{B2i}$, ${a}_{A1i}{\prime}$, ${a}_{B1i}{\prime}$, ${a}_{B2i}{\prime}$, ${a}_{A2i}{\prime}$ of the key factors influencing the choice of strategies by members A and B are both functions of time t.

Establishment of utility matrices for heterogeneous subjects under different combinations of strategies

Based on the above research qualifications, the utility matrix of heterogeneous subjects under different combinations of strategies in shared living spaces is constructed (see Table 1 and Fig. 1).

Table 1 Utility matrix of heterogeneous subjects under different strategy combinations.

Fig. 1

Combination of strategy choices for both sides of the game.

Analysis of the interactive evolutionary process of heterogeneous subjects’ energy-using behavior

Analysis of the dynamics of replication of the subject

(1) Analysis of the replication dynamics of frugal member (A).

Based on the utility matrix of heterogeneous subjects under different combinations of strategies (see Table 1), the expected utility and the average expected utility of the member (A) of the energy-conserving behavior under different behavioral strategies are calculated separately.

A in choosing the expected utility ${E}_{{U}_{A1}}$ of strategy ${S}_{1}$:

$${E}_{{U}_{A1}}=y{U}_{A1}+(1-y){U}_{A1}{\prime}$$

(1)

A in choosing the expected utility ${E}_{{U}_{A2}}$ of strategy ${S}_{2}$:

$${E}_{{U}_{A2}}=y{U}_{A2}{\prime}+(1-y){U}_{A2}$$

(2)

The average expected utility ${E}_{{U}_{A}}$ of A:

$${E}_{{U}_{A}}=x{E}_{{U}_{A1}}+(1-x){E}_{{U}_{A2}}$$

(3)

Then the equation for the replication dynamics of A’s choice of economizing strategy is:

$$F(x)\hspace{0.17em}=\hspace{0.17em}\frac{dx}{dt}=x ({E}_{{U}_{A1}}-{E}_{{U}_{A}})\hspace{0.17em}=\hspace{0.17em}x (1-\text{x}) [y\left({U}_{A1}{-U}_{A2}^{\prime}-{U}_{A1}^{\prime}+{U}_{A2}\right)+{U}_{A1}^{\prime}-{U}_{A2}]$$

(4)

$${\text{F}}^{{{\prime}}}\left(x\right)= (1-2\text{x}) [y\left({U}_{A1}{-U}_{A2}^{{{\prime}}}-{U}_{A1}^{\prime}+{U}_{A2}\right)+{U}_{A1}^{{\prime}}-{U}_{A2}]$$

(5)

Let $F(x)=\frac{dx}{dt}=$ 0, which can be solved by: ${x}_{1}=0, {x}_{2}=1,{ y}^{*}=\frac{{{U}_{A2}-U}_{A1}{\prime}}{{U}_{A1}{-U}_{A2}{\prime}-{U}_{A1}{\prime}+{U}_{A2}}$, according to the stability theorem of the replication dynamics equation, it can be seen that if x is made to be the evolutionarily stable strategy, the conditions that need to be satisfied are:$F(x)=0,{\text{F}}{\prime}\left(x\right)<$ 0. Therefore, three stable states of the evolutionarily stable strategy of member A can be obtained:

When ${y}^{*}=\frac{{{U}_{A2}-U}_{A1}{\prime}}{{U}_{A1}{-U}_{A2}{\prime}-{U}_{A1}{\prime}+{U}_{A2}}$, $F(x)=0$,${\text{F}}^{\prime}\left(x\right)=0$, all x values are steady state; when ${y<y}^{*}=\frac{{{U}_{A2}-U}_{A1}^{\prime}}{{U}_{A1}{-U}_{A2}^{\prime}-{U}_{A1}^{\prime}+{U}_{A2}}$, it is only possible to have two stable state points, i.e. ${x}_{1}=0$,${x}_{2}=$ 1. Since $\text{F}(0)=0,{\text{F}}^{\prime}\left(0\right)<0,F(1)=0,{\text{F}}^{\prime}\left(1\right)>$ 0, therefore ${x}_{1}=0$ is the evolutionarily stable strategy of member A; when ${y>y}^{*}=\frac{{{U}_{A2}-U}_{A1}^{\prime}}{{U}_{A1}{-U}_{A2}^{\prime}-{U}_{A1}^{\prime}+{U}_{A2}}$, also only two stable state points are possible to exist, i.e. ${x}_{1}=0$,${x}_{2}=$ 1. Since $\text{F}(0)=0,{\text{F}}^{{\prime}}\left(0\right)>0,F(1)=0,{\text{F}}{\prime}\left(1\right)>$ 0, therefore ${x}_{2}=1$ is the evolutionarily stable strategy of member A.

(2) Dynamic equations for the replication of a member of the wasteful type (B).

Based on the utility matrices of the subjects of the two types of energy-using behaviors under different combinations of strategies (see Table 1), the expected utility and average expected utility of the members of the wasteful energy-using behaviors (B) under different behavioral strategies are calculated separately.

B in choosing the expected utility ${\text{E}}_{{\text{U}}_{\text{B}1}}$ of strategy ${\text{S}}_{1}$:

$${E}_{{U}_{B1}}=x{U}_{B1}+(1-x){U}_{B1}{\prime}$$

(6)

B in choosing the expected utility ${\text{E}}_{{\text{U}}_{\text{B}2}}$ of strategy ${\text{S}}_{2}$:

$${E}_{{U}_{B2}}=x{U}_{B2}{\prime}+(1-x){U}_{B2}$$

(7)

The average expected utility ${\text{E}}_{{\text{U}}_{\text{B}}}$ of B:

$${E}_{{U}_{B}}=y{E}_{{U}_{B1}}+(1-\text{y}){E}_{{U}_{B2}}$$

(8)

Then the equation for the replication dynamics of B’s choice of wasteful strategy is:

$$F(y)\hspace{0.17em}=\hspace{0.17em}\frac{dy}{dt}=y ({E}_{{U}_{B1}}-{E}_{{U}_{B}})\hspace{0.17em}=\hspace{0.17em}y (1-y)[ x\left({U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}\right)+{U}_{B1}^{\prime}-{U}_{B2}]$$

(9)

Finding the first order derivative of F(y) yields:

$${\text{F}}^{\prime}\left(y\right)= (1-2y)[x\left({U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}\right)+{U}_{B1}^{\prime}-{U}_{B2}]$$

(10)

Let $F\left(y\right)=\frac{dy}{dt}=0$, can be solved by: ${y}_{1}=0$,${y}_{2}=1$,${x}^{*}=\frac{{{U}_{B2}-U}_{B1}^{\prime}}{{U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}}$. According to the stability theorem of the replicated dynamic equations, it can be seen that if $y$ is made to serve as an evolutionary stabilizing strategy, the conditions that need to be fulfilled are:$F(y)=0$,${\text{F}}^{\prime}\left(y\right)<0$. Therefore, the three stabilizing states of the evolutionary stabilizing strategy of mem-ber B can be obtained:

When ${x=x}^{*}=\frac{{{U}_{B2}-U}_{B1}^{\prime}}{{U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}}$, $F\left(y\right)=0$,${\text{F}}^{\prime}\left(y\right)=0$, all $y$ values are steady state; the existence of only two possible stable state points is ${y}_{1}=0$,${y}_{2}=1$ when ${x<x}^{*}=\frac{{{U}_{B2}-U}_{B1}^{\prime}}{{U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}}$; there are also only two possible stable state points ${y}_{1}=0$,${y}_{2}=1$ when ${x>x}^{*}=\frac{{{U}_{B2}-U}_{B1}^{\prime}}{{U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}}$.Since $\text{F}(0)=0$,${\text{F}}^{\prime}\left(0\right)>0$,$F(1)=0$,${\text{F}}^{\prime}\left(1\right)>$ 0, therefore ${y}_{2}=1$ is an evolutionarily stable strategy for member B.

Equilibrium stability analysis of evolutionary processes

Let F(x) = 0, F(y) = 0, by solving the combination of replicated dynamic equations, it can be obtained that there exist a total of five local equilibrium points of this gaming system on the plane $\text{R}=\{(\text{x},\text{y})|0\le \text{x}\le 1, 0\le \text{y}\le 1\}$, i.e., ${\text{E}}_{1}$(0, 0)、${\text{E}}_{2}$(0, 1)、${\text{E}}_{3}$(1, 0)、${\text{E}}_{4}$(1, 1)、${\text{E}}_{5}({x}^{*}, {y}^{*}$), where, ${x}^{*}=\frac{{{U}_{B2}-U}_{B1}^{\prime}}{{U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}},{y}^{*}=\frac{{{U}_{A2}-U}_{A1}{\prime}}{{U}_{A1}{-U}_{A2}{\prime}-{U}_{A1}{\prime}+{U}_{A2}}$.

Determining the evolutionarily stable strategy (ESS) of the whole system can be done by analyzing the determinant of the Jacobi matrix of this system and the positivity and negativity of its traces to determine whether the system is stable at the local equilibrium or not, therefore, taking the partial derivatives of x and y in the combination of replicated dynamical equations, respectively, yields the Jacobi matrix of the gaming system of members A and B, J.

$${\varvec{J}}=\left[\begin{array}{cc}(1-2x)[y\left({U}_{A1}{-U}_{A2}^{\prime}-{U}_{A1}^{\prime}+{U}_{A2}\right)+{U}_{A1}^{\prime}-{U}_{A2} ]& x(1-x)\left({U}_{A1}{-U}_{A2}^{\prime}-{U}_{A1}^{\prime}+{U}_{A2}\right)\\ y(1-y)\left({U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}\right)& (1-2y)[x\left({U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}\right)+{U}_{B1}^{\prime}-{U}_{B2}]\end{array}\right]$$

(11)

If a local equilibrium is an evolutionarily stable strategy (ESS) of a game system, then the determinant det(J) and the trajectory tr(J) of that local equilibrium must satisfy the conditions det(J) > 0 and tr(J) < 0. In particular, if that local equilibrium det(J) > 0 and tr(J) = 0, then that local equilibrium is a saddle point; if that local equilibrium det(J) < 0, tr(J) = 0, then the local equilibrium point is a center point. To determine the stability of these local equilibrium points, i.e., ${\text{E}}_{1}$(0,0)、${\text{E}}_{2}$(0,1)、${\text{E}}_{3}$(1,0)、${\text{E}}_{4}$(1,1)、${\text{E}}_{5}$(${x}^{*}$,${y}^{*}$), the corresponding determinant det(J) and trajectory tr(J) of each local equilibrium point need to be discussed further.

Scenario (1): ${{U}_{B2}>U}_{B1}^{\prime}, {U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}>0,{U}_{B2}^{\prime}<{U}_{B1}\text{ and }$${{U}_{A2}>U}_{A1}{\prime}, {U}_{A1}{-U}_{A2}{\prime}-{U}_{A1}{\prime}+{U}_{A2}>0, {U}_{A2}^{\prime}<{U}_{A1}.$ In this scenario, the game system has two evolutionarily stable points, namely ${\text{E}}_{1}$(0,0) and ${\text{E}}_{4}$ (1,1), i.e., (waste, waste)and (save, save). When the proportion of wasteful subjects among members A and B is relatively large, the game system will gradually converge to the stable point (0, 0). At this time, both members A and B choose the wasteful strategy. When the proportion of economical subjects among members A and B is relatively large, the game system will gradually converge to the stable point (1, 1). At this time, both members A and B choose the economical strategy. That is to say, in the shared living space, the initial scales of the group with economical energy—using behaviors and the group with wasteful energy—using behaviors determine the future evolution direction.

Scenario (2):${{U}_{B2}>U}_{B1}^{\prime},{U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}>0,{U}_{B2}^{\prime}<{U}_{B1}\text{ and }{{U}_{A2}<U}_{A1}{\prime}, {U}_{A1}{-U}_{A2}{\prime}$ ${U}_{A1}{-U}_{A2}{\prime}-{U}_{A1}{\prime}+{U}_{A2}<0,{U}_{A2}{\prime}>{U}_{A1}.$ In this case, there is no evolutionary equilibrium point of the system under this condition. In a shared living space, when the utilities obtained by the two players in a game under different strategy combinations meet the conditions of Scenario 2, a series of guiding strategies should be adopted as much as possible to prompt the game system to evolve towards the stable equilibrium point (1, 1) that we expect to reach.

Scenario (3): ${{\text{U}}_{\text{B}2}<\text{U}}_{\text{B}1}^{\prime},{\text{U}}_{\text{B}1}-{\text{U}}_{\text{B}2}^{\prime}-{\text{U}}_{\text{B}1}^{\prime}+{\text{U}}_{\text{B}2}<0\text{ and }$, ${\text{U}}_{\text{B}2}^{\prime}>{\text{U}}_{\text{B}1}\text{ and} {{\text{U}}_{\text{A}2}>\text{U}}_{\text{A}1}^{\prime},$${\text{U}}_{\text{A}1}{-\text{U}}_{\text{A}2}^{\prime}-{\text{U}}_{\text{A}1}^{\prime}+{\text{U}}_{\text{A}2}>0{\text{U}}_{\text{A}2}^{\prime}<{\text{U}}_{\text{A}1}$. In this case, the evolution strategy of the game system is in a state of dynamic change and cannot reach the evolutionary stable equilibrium strategy.

Scenario (4): ${{U}_{B2}<U}_{B1}^{\prime}, {U}_{B1}-{U}_{B2}^{\prime}-{U}_{B1}^{\prime}+{U}_{B2}<0\text{ and } {U}_{B2}^{\prime}>{U}_{B1}\text{ and }{{U}_{A2}<U}_{A1}{\prime},$ ${U}_{A1}{-U}_{A2}{\prime}-{U}_{A1}{\prime}+{U}_{A2}<0, {U}_{A2}{\prime}>{U}_{A1}.$ In this case, The game system has only two evolutionarily stable points, namely ${\text{E}}_{2}$(0,1) and ${\text{E}}_{3}$(1,0), i.e., (waste, save)and (save, waste). At this stage, energy-saving and energy-wasting behaviors coexist: some individuals conserve energy due to policy incentives or habits, while others persist in wasting due to low costs or weak awareness, forming a dynamic equilibrium at the locally stable points (0,1) or (1,0).

Methodology

Questionnaire design

The questionnaire was used to obtain empirical data on the total utility functions obtained by subjects of shared living space when they choose different energy-using behaviors. Graduate students were selected as the subjects of the survey, the time of student communication was divided into three stages. For graduate students, there are three academic years. One grade may correspond to one stage. The first grade corresponds to T1 period, the second grade corresponds to T2 period, and the third grade corresponds to T3 period.

The questionnaire consists of three main parts: first, the basic information of the respondents. The second is the description of some specific energy use behaviors, please refer to Table S5 in Appendix 1 for details. The third is about the factors that affect the energy use behavior of heterogeneous subjects in shared living space under different strategy combinations. To make it easier to express the different strategy combinations, the questionnaire provides 2 hypothetical scenarios. See Table 2 for details.

Table 2 Content of specific scenario assumptions.

The questionnaire inquired about which factors would motivate the respondents to conserve energy under the above two scenarios, which factors would motivate the respondents not to conserve energy, and the overall satisfaction level of the respondents’ needs when they chose to conserve or not to conserve energy, see Table 3 for details. The questionnaire uses a 5-point Likert scale, in which the researchers are asked to rate the extent to which different factors influence their energy use behavior and the overall satisfaction level of choosing different strategies in different situations, where 1 means "not at all influential" or "not at all satisfying", 5 means “very influential” or “very satisfied”.

Table 3 Measurement of influencing factors.

After the initial questionnaire was designed, to ensure that it was easy to understand and fill out, the researchers invited some students outside the research field to pre-fill the questionnaire. They identified the words that were difficult to understand and the unclear expressions in the questionnaire and made modifications. For example, some terms were too professional, such as "perceived behavioral control". Even at the beginning of the questionnaire design, the researchers considered this issue and used the definition of this term to describe the item. However, some students still found it a bit difficult to understand. Therefore, the researchers modified the term several times and communicated with the students who originally had questions about it, and finally determined the question as "The choice of energy—using behavior in the dormitory completely depends on me."

A pre—survey was conducted using the modified questionnaire. A total of 100 questionnaires were distributed in this process. Through the analysis of the pre-survey questionnaires, it was found that although the respondents were informed that the questionnaire results would be kept confidential and only used for scientific research, some respondents still did not give definite answers to the items slightly related to personal privacy, such as the average monthly living expenses. So, the researchers changed this item from a fill—in—the—blank question to a multiple—choice question, that is, they made a stepped division of the living expenses usage. Some respondents also had questions about whether the question "How many hours do you spend in the dormitory on average every day?" included sleeping time. To eliminate this confusion, the researchers added a note "including sleeping time" after the question, because energy consumption also occurs during sleep, such as charging mobile phones and using air—conditioners. After repeated modifications, the final version of the questionnaire was determined in this paper.

Distribution of questionnaires

This paper takes graduate student dormitories as a concrete research scenario for shared living spaces, with the survey subjects being graduate students. The questionnaire was distributed to graduate students at a university in Guangxi. A dormitory contains four graduate students living together, and the main electrical equipment includes air conditioning, lights, computers, mobile phones, and electric fans. We randomly selected 380 dormitories and communicated with all the students in each dormitory through the dormitory director to explain the purpose of the study and ask them if they were willing to participate in the survey. A total of 1,500 people agreed to participate in the survey.

When distributing the questionnaire, both online and offline methods were used. The online approach is to develop an online survey platform for office workers of Chinese companies, schools and government departments. Standardized electronic questionnaires are made and encrypted access links with unique identification codes are generated. Then, investigators display QR codes and short links on paper flyers in student dormitories and invite students to fill them out face to face.

The offline method is as follows: Considering that many students go out on weekends and need to attend classes or study during weekdays, researchers chose to conduct door-to-door surveys after 9 PM on workdays. During the survey, they proactively sought help from school and dormitory administrators, obtained a distribution table of dormitories by grade from the dormitory manager, and conducted the survey with the permission of the dormitory manager.

To improve the effective recovery rate of the questionnaire, the following measures are taken: ① Train the investigators to clarify the research purpose and precautions and reduce operational errors; ② Check the completeness during the recovery process and fill in the missing information in a timely manner. When answering the respondents’ questions, only provide explanations of the questions and avoid guiding the answers. Both offline and online methods of completion were used and the research was conducted from October-December 2023.

Processing of data

Generalized fixed-order logit regression analysis was used to determine the initial values of each parameter in the total utility function obtained when subjects chose different energy-use behaviors during the periods T1, T2, and T3. Subsequently, matlab numerical simulation was used to empirically analyze the interaction process of the subject’s energy-use behaviors and to determine the specific conditions for the interaction stability of the subject’s energy-use behaviors during the periods T1, T2, and T3, to elucidate the interaction mechanism of the subject’s energy-use behaviors in the shared living space. The detailed information of the software used in our research is as follows: the full name of the software is MATLAB (MATrix LABoratory), version R2023b (23.2), and the official download link is https://ww2.mathworks.cn/products/new_products/release2023b.html.

Ethical approval

Ethical approval for this study was obtained from the institutional review board (committee set by Guangxi University of Science and Technology). All methods were performed in accordance with the relevant guidelines and regulations set by the institutional review board. Informed consent was obtained from all the participants and /or their legal guardians.

Results

Descriptive statistical analysis

A total of 1500 questionnaires were distributed, and 1238 valid questionnaires were returned after excluding 262 invalid questionnaires, with an effective recovery rate of 82.53%. Cronbach’s alpha coefficient and KMO and Bartlett’s spherical test were used to assess the reliability and validity of the questionnaire, respectively. The results showed that the Cronbach’s alpha coefficients of the economizing and wasting groups under each strategy combination were all greater than 0.8, the P-values of Bartlett’s spherical test were all less than 0.001, and the KMO values were all greater than 0.8, which indicated that the questionnaires had high reliability and validity (see Fig. 2).

Fig. 2

Descriptive statistics of demographically characterized variables.

Determination of initial value of subject size

In this paper, the ratio of the number of samples of energy-saving and wasteful energy-using behaviors is taken as the initial value of the subject size share of the two. Subsequently, the sample sizes of each group at different periods of heterogeneous subject interactions were counted and the ratios between them were calculated. The sample size ratios of conservation-oriented and waste-oriented energy use behaviors for periods T1, T2, and T3 were: 0.49:0.51,0.41:0.59, and 0.46:0.54, respectively. Here, period T1 represents the time spent living with roommates for 0–1 year, period T2 represents for 1–2 years, and period T3 for 2–3 years. Detailed data are shown in Table S6 of the Appendix 1.

Determination of the initial values of the coefficients of the influencing factors in the utility function

The value of the coefficients of each influential factor depends on the results of the regression analysis, with the coefficients of the significant factors being the regression coefficients and the coefficients of the non-significant factors being 0. The regression analysis was carried out using the heterogeneous subject’s satisfaction with the different combinations of strategies as an explanatory variable and the correlates as explanatory variables. The regression analysis results of heterogeneous subjects in different periods of interaction and under different strategy combinations are shown in Tables S7 to S10 in the Appendix 1.

Simulation analysis of the interactive evolution process of heterogeneous subjects’ energy use behavior

Based on the initial values of the simulation parameters of the interaction evolution process of the heterogeneous subject’s energy-using behavior set above, matlab numerical simulation was used to simulate and analyze the interaction evolution process of the heterogeneous subject’s energy-using behavior, as described below.

Time spent with roommates 0–1 year

(1) Simulation analysis of the evolution process at the initial value state.

The simulation analysis based on the above empirical data is shown in Fig. 3, where x represents the subjects of energy—saving behavior and y represents the subjects of energy—wasting behavior. It can be seen that in the graduate student dormitories, when the time for heterogeneous subjects to get along with their roommates is 0–1 year, if no intervention is applied, the game system will tend to the equilibrium state of (1, 0), that is, (save, waste), which is not the result we expect.

Fig. 3

Results of the interactive evolution of heterogeneous subjects’ energy-using behaviors in the T1 period.

(2) Simulation analysis of the evolution process when changing the initial values of parameters.

If only one aspect of social demand utility, environmental demand utility, effort utility, economic demand utility, and comfort demand utility is increased respectively in T1, the strength of its effect remains unchanged. From the evolution results of the game system when the corresponding variables take different values in T1 (see Fig. 4), it is largely impossible to promote the evolution of the game system to the stabilization point (1,1).

Fig. 4

Evolutionary results of the gaming system when the corresponding variables take different values in the period T1.

If the utilities of social needs, environmental protection, economic and comfort needs, and the efforts made are changed simultaneously at time T1, it can be achieved by simultaneously improving interpersonal relationships, reducing comfort, increasing attention to energy issues, increasing energy costs, reducing the efforts made to change energy-using habits, and enhancing the perceived behavioral control. The values of these variables are decreased or increased by 0.5, 1.0, 1.5, 2.0, and 2.5 units respectively according to the needs, while still keeping their intensity of influence unchanged. As can be seen from Fig. 5, the strategy of improving social, environmental, economic and comfort needs as well as the utility of efforts can largely promote the heterogeneous subjects in graduate dormitories to choose energy-saving strategies during the T1 period.

Fig. 5

Evolutionary results of the gaming system when multiple corresponding variables are simultaneously changed to take different values in period T1.

Time spent with roommates 1–2 years

(1) Simulation analysis of the evolution process at the initial value state.

Based on the above empirical data, the simulation analysis of the interactive evolution of heterogeneous subjects’ energy-use behavior in the T2 period shows (see Fig. 6) that, without intervention, the long-term evolution will tend to the non-energy-saving equilibrium state of (0, 0).

Fig. 6

Results of the interactive evolution of heterogeneous subjects’ energy-using behaviors in the T2 period.

(2) Simulation analysis of the evolution process when changing the initial values of parameters.

Changing only the economic demand utility

If the economic demand utility is only reduced at T2, this can be achieved by increasing the variable of energy costs. As can be seen from Fig. 7a, the evolution of the game system to the stable point (1,1) can be greatly promoted by simply increasing the value of the variable energy cost. It is worth noting that in real life, if energy costs are to be increased, they should be kept within a reasonable range.

Fig. 7

Evolutionary results of the gaming system when the corresponding variables take different values in the T2 period.

(3) Change only the comfort demand utility

If the value of comfort is taken at T2 is reduced by 0.5, 1.0, 1.5, 2.0, and 2.5 units, respectively, the strength of its action is still kept unchanged. As can be seen from Fig. 7b, if only the strategy of reducing comfort is adopted, it can greatly promote the heterogeneous subjects in graduate dormitories to choose energy-saving strategies in T2 period. Moreover, it is worth noting that when guiding the heterogeneous subjects in the shared living space to carry out energy saving, they should not just reduce people’s demand for comfort, but should carry out energy saving based on satisfying people’s basic demand for comfort.

Time spent with roommates 2–3 years

(1) Simulation analysis of the evolution process at the initial value state.

Based on the above empirical data, the simulation analysis of the interactive evolution of heterogeneous subjects’ energy use behaviors in the T3 period shows (see Fig. 8) that, without intervention, the long-term evolution will converge to the non-energy-saving equilibrium state of (0, 0), which is not in line with the desired energy-saving results.

Fig. 8

Results of the interactive evolution of heterogeneous subjects’ energy-using behaviors in the T3 period.

(2) Simulation analysis of the evolution process when changing the initial values of parameters.

From the evolution results of the game system when the corresponding variables take different values in T3 (see Fig. 9), if only one aspect of the social demand utility or comfort demand utility is reduced in T3, by changing the two variables of group identity and comfort, it is largely able to promote the evolution of the game system to the stability point (1,1).

Fig. 9

Evolutionary results of the gaming system when the corresponding variables take different values in the period T3.

On the other hand, if only the utility of effort paid is reduced at T3, this can be done by increasing the variables of energy-using habits and subjective norms, with the values of energy-using habits being increased by 0.5, 1.0, 1.5, 2.0, and 2.5 units, respectively, while still keeping the intensity of their effects unchanged. As can be seen from Fig. 10, if the values of energy use habits and subjective norms are appropriately increased respectively, it is difficult to promote the evolution of the game system to the stable point (1,1).

Fig. 10

Evolutionary results of the gaming system when the corresponding variables take different values in the period T3.

However, if the environmental demand utility is only increased at T3, it can be done by increasing. As can be seen from Fig. 11, if the value of the variable individual norm is appropriately increased, it can largely promote the evolution of the game system to the stable point (1,1).

Fig. 11

Evolutionary results of the gaming system when individual norms take different values in period T3.

Discussion and analysis

Discussion and analysis of the the time spent with roommates 0–1 year

Initial value state

When the game system is in the T1 period and not subject to external intervention, the system will eventually evolve to the equilibrium state of (1, 0) over time, which means that in the absence of external incentives and constraints during the 0–1 year period of cohabitation with roommates in the shared living space, even if one party adopts positive energy-saving measures, the other party will not follow them accordingly, which results in the overall failure to achieve the desired energy-saving effect. This is because during the 0–1 year period of cohabitation with roommates, although there is a certain degree of willingness to cooperate and initial contact, due to the shallow mutual understanding and weak foundation of trust, individuals are more likely to make decisions based on personal interests rather than consider issues from the perspective of collective benefits³². Second, during the 0–1 year period of cohabitation with roommates, residents mainly display shallow interactions with each other and try to find common ground to build emotional bonds. However, such social dynamics are not sufficient to overcome the resistance held by individuals to change established habits, especially when these changes require extra efforts or sacrifices³³. Therefore, in the absence of positive external guidance, it is difficult to achieve the goal of effective energy management by relying on spontaneous individual adjustments alone, and the necessary policy guidance and incentives are needed to promote changes in residents’ behavior.

Changing the state of the initial value of the parameter

Changing only the social demand utility, through the strategy of improving interpersonal relationships, does not, to a large extent, ensure that heterogeneous subjects all choose the stabilizing strategy of energy conservation during the 0–1 year period of cohabitation with roommates. This finding was incongruent with the research results reported by Li et al.³⁴. This is because although positive interpersonal relationships can promote cooperation and communication among heterogeneous subjects in a shared living space, this does not necessarily lead to a uniform acceptance of energy-saving behaviors. Each individual’s energy use habits may be deeply rooted and influenced by multiple factors such as personal lifestyle, economic conditions, and technology availability³⁵. For example, some subjects may ignore the importance of energy conservation due to the pursuit of comfort, while others may not be able to take effective energy conservation measures because they lack the necessary awareness or knowledge of energy conservation. In this process, the behavioral patterns of different subjects will have an impact on each other, and if some members do not actively participate in energy conservation, it may weaken the energy-saving atmosphere of the whole shared living space.

Changing only the environmental demand utility, through the strategy of increasing attention to energy issues, largely fails to motivate all heterogeneous subjects to choose energy-saving strategies during the 0–1 year period of cohabitation with roommates in a shared living space. This finding was incongruent with the research results reported by Chen and Hu³⁶, for the following reason: although the increase in attention can make subjects realize the importance of energy issues, it is not enough to change their daily behavioral patterns. Various heterogeneous subjects have different habits, personal preferences, and acceptance of energy-saving measures, which together contribute to their behavioral choices. In addition, energy-saving behaviors often require additional self-restraint and long-term persistence, which is a challenge for graduate students whose self-control is still developing. What’s more, when there are subjects in the group who begin to show energy-saving behaviors, this can serve as a social signal to encourage other members to choose energy-saving behaviors; conversely, if the majority of the people do not show an obvious willingness to save energy, then even if there are a few subjects who want to practice energy-saving behaviors, they will feel isolated and helpless.

Changing only the utility of effort exerted, respectively reducing the effort exerted for energy use habit change and enhancing the degree of perceived behavioral control to carry out, to a large extent, is not able to motivate the heterogeneous subjects in the shared living space in the T1 period to all choose energy-saving strategies, this finding was incongruent with the research results reported by Wang et al.³⁷. The reason for this is that, on the one hand, while efforts to reduce the change in energy use habits can reduce psychological and physical barriers to behavioral change, subjects may not take the initiative to adopt energy-saving measures if they do not pay enough attention to energy conservation or lack the necessary knowledge and skills to do so. On the other hand, enhancing the degree of perceived behavioral control can help people better understand and evaluate their behavior, which may potentially facilitate energy-saving behavior. However, in shared living spaces, individual behaviors are often largely influenced by others, and if no one around them has formed good energy-saving habits, then even if a particular subject has a strong perception of perceived behavioral control, he or she may be reluctant to make changes for fear of going against the collective behavior.

Changing only the economic demand utility, through the strategy of increasing the cost of energy use, largely fails to motivate all the heterogeneous subjects in the shared living space in the T1 period to choose the energy-saving strategy, which is consistent with the findings reported by Ohler et al.³⁸. The reason for this is that increasing the cost of energy use may affect some economically more sensitive groups, causing them to reduce their expenses by reducing unnecessary energy consumption. However, for those individuals who are better off or not price-sensitive, such economic incentives may have little effect, and economic incentives alone may not be sufficient to change their behavioral patterns. It is worth noting that when price-sensitive individuals in the same shared living space see that others are not adjusting their energy consumption patterns as a result of rising energy costs, the subjects who were considering energy conservation may abandon the idea, as there is no clear benefit to them in doing so when energy costs are shared equally.

Changing the comfort demand utility only, by reducing the comfort level as a strategy, largely fails to motivate all the heterogeneous subjects in the shared living space in the T1 period to choose energy-saving strategies, which is inconsistent with the results of the study by Yoo et al.³⁹, due to the following reasons: by reducing the comfort level as a strategy only, it ignores the basic physiological and psychological needs of human beings, as well as the individual’s subjective feelings and tolerance of comfort. In shared living spaces, each subject has different definitions and expectations of comfort; some people may be willing to tolerate lower temperatures to save energy, while others may need a more suitable environment to maintain comfort and quality of life. Therefore, simply lowering the comfort standard may lead to dissatisfaction or even resistance to energy conservation measures by some people. In addition, during the 0–1 year period of cohabitation with roommates, when mutual understanding and trust have not yet been fully established, a mandatory reduction of the comfort level to promote energy conservation may cause resistance and dissatisfaction among some subjects, thus hindering the implementation of energy conservation strategies.

At the same time, the strategies of improving interpersonal relationships, reducing comfort, increasing attention to energy issues, increasing energy costs, reducing the efforts made to change energy habits, and enhancing perceived behavioral control is largely able to motivate the heterogeneous subjects in the shared living space to adopt the energy-saving strategy in the T1 period because: during the 0–1 year period of cohabitation with roommates, improving interpersonal relationships can reduce resistance caused by misunderstandings or distrust. Resistance and lay a good social foundation for the implementation of energy-saving measures; at the same time, increasing attention to energy issues can increase people’s awareness of the importance of energy saving, thus promoting them to take action in their daily lives; increasing energy costs can directly reflect the economic benefits of energy saving and stimulate the subjects to take action; and decreasing the efforts made to change the energy use habits and increasing the perceived behavioral control reduce barriers to energy-saving actions at both the psychological and behavioral levels. Moreover, in the early stage of interpersonal interaction, people are more easily influenced by new information and other people’s behaviors, and the energy-saving awareness and habits formed at this time are easier to maintain and spread. Therefore, a combination of these strategies can create an environment conducive to the development of energy-saving behaviors during the 0–1 year period of cohabitation with roommates, which can lead to the general selection of energy-saving strategies by heterogeneous subjects in shared living spaces.

Discussion and analysis of the time spent with roommates 1–2 years

Initial value state

During the 1–2 years period of cohabitation with roommates, even if both parties are willing to open themselves and share information and emotions, if there is a lack of external intervention, the gaming system will eventually converge to the non-ideal equilibrium state of (0, 0), which suggests that even in the case of more harmonious social relations and adequate information exchange, individuals may not spontaneously choose environmentally friendly and energy-saving behaviors out of their self-interests to maximize behavioral patterns. This is because when people build trust and are willing to share personal information and emotions⁴⁰, this does not necessarily translate into increased energy-saving behaviors, although it can help to enhance cohesion and a sense of belonging within the community. Moreover, without proper guidance and support, even a social network with a high degree of mutual trust can struggle to overcome the negative impacts of individuals pursuing short-term convenience and comfort. Therefore, to achieve more sustainable development goals, this unfavorable evolutionary direction needs to be altered using policy guidance, incentive mechanism design, or education and awareness-raising to promote the formation of more positive energy use habits.

Changing the initial value of a parameter

Changing only the economic demand utility, by increasing the cost of energy use as a strategy, is largely capable of inducing all heterogeneous subjects in the shared living space in the T2 period to choose energy-saving strategies. This finding is consistent with the research results reported by Steg et al.⁴¹ because, during the 1–2 years period of cohabitation with roommates, subjects in a shared living space usually have already established rules and mutual expectations for common compliance. At this point, their energy consumption decisions can be more significantly influenced by adjusting economic incentives, such as increasing the cost of energy use. This is because as costs rise, individuals feel more financial pressure, which may motivate them to look for ways to reduce energy consumption, such as using energy-efficient equipment and reducing air-conditioning hours. In addition, in shared living spaces where relationships are stable, members may have developed some degree of interdependence and community identity. The presence of such social capital means that when energy efficiency measures are introduced, members may be more inclined to cooperate to jointly cope with rising energy costs. It is worth noting that purely economic incentives may not be sufficient to change people’s energy consumption behavior in a lasting way, so when implementing the strategy of increasing energy costs, it should be combined with other non-economic incentives and take into account the affordability of different subjects, to prevent excessively high costs from exerting too much financial pressure on certain groups. At the same time, the fairness and transparency of the fee increase should be ensured to avoid unnecessary contradictions and conflicts.

By solely reducing comfort levels, it is largely possible to encourage the heterogeneous subjects in university student dormitories to adopt energy-saving strategies during the T2 period, This finding was congruent with the research results reported by Aqilah et al.⁴². The reason lies in: when the relationships among subjects in university student dormitories reach a stable phase, they have already adjusted their comfort levels to some extent to accommodate each other’s living habits, forming a pattern of mutual adaptation and compromise. At this point, reducing comfort levels as part of an energy-saving strategy may be more readily accepted by the subjects, as they have already experienced mutual adaptation. When they see other members willing to sacrifice comfort for energy savings, individuals are more likely to follow and adopt similar energy-saving behaviors, which will form a positive social norm, thereby motivating more people to follow. However, the tolerance for comfort levels can be influenced by differences in physiological and psychological needs. Although subjects may compromise on comfort levels during the 1–2 years period of cohabitation with roommates, this does not mean they can tolerate low comfort levels indefinitely. Therefore, when implementing energy-saving strategies that reduce comfort levels, it is essential to fully consider the differences in physiological and psychological needs among subjects and seek a balance to avoid excessively lowering comfort levels that could affect their quality of life.

Discussion and analysis of the results of the time spent with roommates 2–3 years

Initial value state

When the subjective relationship between residents in the shared living space reaches a stable phase during the 2–3 years period of cohabitation with roommates, the game-theoretic system tends to trend towards (0, 0), a non-desired equilibrium state. This suggests that in the absence of external intervention, individuals are more inclined to adopt behavioral patterns that are not conducive to energy conservation and emission reduction as the interaction between residents decreases and the degree of intimacy diminishes. This is because when social ties become looser, people’s attention to common energy-saving goals and willingness to cooperate decline. Thus, even in groups that have previously established good cooperative relationships, once faced with spatial separation and reduced frequency of interactions, the previously accumulated trust and social ties may not be sufficient to maintain positive energy use habits⁴³, which further exacerbates the difficulty of achieving collective energy conservation goals. Moreover, at this stage, residents may no longer exchange information or share resources as frequently as before, which reduces opportunities for mutual monitoring and support, a change that not only weakens the willingness to comply with energy-saving and emission-reduction commitments but also reduces the likelihood of spreading energy-saving practices through social networks. Thus, while there may have been some degree of positive interactions in the early stages, these positive influences quickly dissipate during the 2–3 years period of cohabitation with roommates, rendering the social mechanisms that could have promoted energy conservation ineffective, and ultimately returning the overall pattern of energy consumption to a more individualized and less sustainable state.

Changing the state of the initial value of the parameter

The strategy of reducing group identity largely promotes the adoption of energy-saving strategies by heterogeneous subjects in graduate dormitories during the T3 period, this finding was congruent with the research results reported by Lin and Jia⁴⁴. The reason is that during the 2–3 years period of cohabitation with roommates, the original group structure and cohesion begin to disintegrate, leading to a decrease in group identity. This provides an opportunity for introducing new behavioral patterns. Unrestrained by previous group norms, individuals may adopt a more open attitude toward new rules and behaviors, showing higher acceptance and adaptability to new energy-saving strategies. Moreover, under mutual influence, individuals are more likely to spread and adopt these new energy-saving strategies. Additionally, when group identity decreases, individuals may no longer sacrifice personal interests or ignore environmental issues to maintain harmony within the group as they did before. Instead, they may evaluate their own behaviors more independently and tend to choose actions they believe are beneficial for both themselves and the environment, such as energy-saving behaviors. This increased independence, combined with the dynamic process of mutual observation and imitation among individuals, can facilitate the spread and popularization of energy-saving behaviors throughout graduate dormitories.

By merely reducing comfort, it is largely possible to encourage the heterogeneous subjects in university dormitories to choose energy-saving strategies during the T3 period, this finding was congruent with the research results reported by Petidis et al.⁴⁵. The reason lies in: during the 2–3 years period of cohabitation with roommates, the subjects in university dormitories are about to end their shared life together, and their expectations for comfort may no longer be as strong as before, which provides a possibility to reduce comfort levels to achieve energy savings. Secondly, when the relationship between subjects is about to dissolve, the existing bonds and consensus may begin to weaken, and the degree of mutual influence among individuals will also decrease. In such circumstances, the subjects’ motivation and willingness to maintain the original comfort standards may decline because they know that this period of shared living is coming to an end. Therefore, they may be more willing to accept slightly lower comfort levels to support energy-saving behaviors. However, this approach also carries certain risks. During the 2–3 years period of cohabitation with roommates, subjects may feel uneasy due to uncertainty about future living environments, and reducing comfort might be seen as an additional burden on their current state, leading to dissatisfaction or resistance. Thus, when implementing this strategy, it is necessary to fully consider the mutual influence and psychological state of the subjects, ensuring that the measures taken can promote energy savings without causing unnecessary conflicts.

Strategies that appropriately increase energy habits and subjective norms, respectively, are largely unable to motivate all heterogeneous subjects in shared living spaces in the T3 period to choose energy-saving strategies. This finding is consistent with the research results reported by Steg et al.⁴¹. In shared living spaces, when the relationship between subjects is about to dissolve, the original relational bonds and consensus begin to weaken, and the interaction and mutual influence between individuals decreases, making it difficult to maintain commonly observed norms and habits. When members of a shared living space no longer share common interests or goals, they may no longer be willing to change their behavior for the benefit of the group as a whole. In this case, as the life of shared living is coming to an end, the subject may also be less motivated to maintain the original energy-use habits and subjective norms, and at this time, if an attempt is made to promote the choice of energy-saving strategies among residents in the shared living space by enhancing the energy-use habits and subjective norms, it is difficult to achieve the expected results because the mutual influence among individuals has been weakened, and they may be more inclined to keep the status quo and be unwilling to, for the sake of energy-saving change the original habits and norms.

Changing only the environmental demand utility, the strategy of appropriate individual norms is largely able to motivate all the heterogeneous subjects in the shared living space in the T3 period to choose energy-saving strategies, which is consistent with the findings reported by Liu et al.⁴⁶. This is because during the 2–3 years period of cohabitation with roommates, although individuals may no longer be as strongly influenced by group norms and expectations, their decisions are still influenced by the behaviors and attitudes of those around them. During this phase, individuals have increased autonomy and are more inclined to choose their path of action based on their values and interests. If the utility of elevating environmental demand enables individuals to recognize the long-term value and personal benefits of energy-saving behaviors, such as cost reduction and comfort enhancement, then they are more likely to be inclined to adopt these strategies. Moreover, even in the relationship dissolution period, the mutual influence among individuals still exists, and this positive demonstration effect can further enhance individuals’ willingness to adopt energy-saving behaviors when they see others adopting energy-saving measures. Therefore, by enhancing the environmental demand utility and combining it with inter-individual interactions, the prevalence of energy-efficient behaviors can be more reliably promoted throughout the shared living space.

Conclusions and policy recommendations

Conclusion

Under the current background of China’s goal of "achieving carbon peak by 2030 and carbon neutrality by 2060", it is of great significance to guide people in shared living spaces to implement energy-saving behaviors. However, because the interactive evolution mechanism of heterogeneous subjects’ energy-use behaviors in shared living spaces is still unclear, energy managers can’t formulate more reasonable and effective energy-saving guidance strategies to achieve energy conservation and emission reduction in buildings in shared living spaces. However, due to the unclear mechanism of the interactive evolution of energy use behavior of heterogeneous subjects in shared living spaces, energy managers are unable to formulate more reasonable and effective energy-saving guidance strategies to realize energy conservation and emission reduction in buildings in shared living spaces. Therefore, this study aims to investigate the interactive evolution mechanism of heterogeneous subjects’ energy use behaviors in shared living spaces, to provide a reference for energy managers to formulate corresponding energy-saving guidance strategies.

Based on the evolutionary game theory, this paper relaxes the assumption that the utility obtained by the subject when choosing the corresponding strategy is unchanging and instead considers the utility as changing with the change of the interaction length between the two sides of the game, and at the same time, it introduces the idea of "human’s behavior depends on his psychological needs" in the self-determination theory, and quantifies the utility under different combinations of strategies in the shared living space in five dimensions: "social needs, environmental needs, economic needs, comfort needs, and efforts", to construct a mechanism model of the interactive evolution of heterogeneous subjects’ energy-using behaviors in shared living space. Through the analysis of the replication dynamics of heterogeneous subjects and the equilibrium stability analysis of the evolution process of heterogeneous subjects’ energy use behavior, it is found that there is an evolutionary stabilization point of the game system where heterogeneous subjects all choose the conservation strategy, and to reach this stabilization point, two conditions need to be satisfied at the same time: (1) Under different strategy combinations, even if one party chooses the same strategy, the utility gained by that party when both parties choose the same strategy is greater than the utility gained by that party when both parties choose different strategies. Moreover, the sum of the utilities gained by either party when both parties choose the same strategy combination is greater than the sum of the utilities gained by that party when both parties choose different strategies. (2) the probability value of choosing the frugal strategy by both parties of the game needs to fall in the region consisting of the saddle point, (1,1), (0,1), and (1,0).

Finally, taking the student dormitory as an example, the initial values of the simulation parameters of the interaction evolution model of the heterogeneous subject’s energy-use behavior obtained through the questionnaire survey, and using matlab numerical simulation to simulate and analyze the interaction evolution process, it is found that: without exerting any intervention, it is difficult to reach the stabilization point where both parties choose the conservation-oriented strategy for the game system composed of the heterogeneous subjects in the shared living space, and if the probability of both parties choosing the conservation-oriented strategy is increased, it should be adopted according to the different periods of interaction of the heterogeneous subjects. Specifically, when the time spent with roommates is 0–1 year, the utility of social demand, environmental demand, economic demand, comfort demand, and effort can be changed at the same time; when the time spent with roommates is 1–2 years, the utility of economic demand and comfort demand can be changed; and when the time spent with roommates is 1–2 years, by changing social demand utility, comfort demand utility, and environmental demand utility.

Responses and recommendations

Based on the results of the above analysis and discussion, this paper puts forward the following countermeasures and recommendations:

• To establish an effective communication mechanism. Schools can make use of student groups such as student councils, hostel staff, and counselors to organize regular communication among dormitory members on their desired indoor air conditioning setting temperatures. Through face-to-face communication, each member can express his/her needs and feelings, and jointly discuss the air conditioning setting temperature that can meet the comfort needs of most members and also realize the goal of energy saving. Encourage dormitory members to actively express their needs and feelings about indoor temperature in their daily interactions so that problems can be identified and solved promptly. For example, a public message board can be set up in the dormitory to facilitate members to leave messages at any time to share their comfort needs and air-conditioning usage so that other members can understand and refer to them.

• (2)To implement environmental education programs. Organize educational activities related to energy conservation and emission reduction to raise students’ attention to energy issues, and demonstrate the dual economic and environmental benefits of energy conservation through practical cases, such as lectures, seminars, competitions or thematic activities, etc., provide course training on energy conservation knowledge and skills, and add energy conservation-related elective courses. In addition, we will give full play to the role of various public opinion media in publicizing and guiding students, conveying information on energy dependence and the hazards of energy shortage to deepen their knowledge of energy issues and enhance their sense of responsibility for energy conservation.

• (3)To formulate rational energy use policies. Set clear rules and standards for energy use, such as limiting unnecessary power consumption and promoting the use of energy-saving equipment, to reduce energy costs and improve overall energy efficiency. Reasonably adjust electricity consumption charges according to the actual situation, such as implementing separate billing for high-power electrical appliances, reducing or canceling free electricity credits, and raising electricity consumption charges. In addition, the extra charges will be used to recognize or provide material incentives to individuals or teams that have made significant contributions to energy conservation, to motivate them to continue to improve their energy-use habits.

• (4)To strengthen the ability of self-management. Encourage roommates to remind each other of bad energy habits and learn good habits from each other to form an energy-saving atmosphere within the dormitory. Guide students to recognize the impact of individual behavior on collective interests, and cultivate them to consciously adjust their behavioral habits in daily life to achieve a balanced state that meets their own needs without harming the interests of others. Encourage dormitory members to take the initiative to participate in the management and supervision of daily life, such as taking turns to serve as housemasters or energy-saving supervisors, etc., to cultivate a sense of responsibility and self-discipline, and to identify and solve problems promptly.

Limitations and outlook

Compared with previous studies, this paper not only focuses on the energy-saving behavior itself, but also explores in depth the influence of social psychological factors such as interpersonal relationships, group identity, and comfort level on energy-saving behavior, which is relatively rare in previous studies. In addition, this study also considers that the utility gained by the subject when choosing the corresponding strategy changes with the length of interaction between the two parties of the game, which provides a dynamic perspective to observe the change of energy-saving behavior by introducing the change of interpersonal interaction time and interaction stage, which is also rare in previous static studies. However, this paper also has some limitations. First, the data source is relatively limited to master’s degree students at a single university, which may restrict the generalizability of the findings. Second, the purely time-based segmentation of relational stages, while avoiding assumptions about subjective relational states, fails to capture the actual contextual dynamics (e.g., whether interactions are in the formation, stability, or dissolution phase), potentially obscuring nuanced differences in how interpersonal dynamics shape behavioral outcomes.

Future research should incorporate qualitative interviews, behavioral tracking, or mixed-method approaches to explicitly identify relational phases and validate the contextual validity of time-based classifications, while also expanding sample diversity to enhance external validity.