IoT driven healthcare monitoring with evolutionary optimization and game theory

Abstract

In this paper the game theory procedures are applied for healthcare monitoring systems and it is analysed using two types of evolutionary algorithms that incorporate Artificial Intelligence (AI) based events. As most of the existing approaches face challenges in establishing real-time connectivity, optimizing decision-making processes, and minimizing latency in Internet of Things (IoT)-based healthcare applications the limitations needs to be addressed. Hence with analytical equivalences that are crucial in game theory, a unique system model is developed using a deterministic framework where four key performers are strategically connected to improve decision-making and security against potential data breaches. By incorporating two evolutionary algorithms, the proposed approach optimizes the state of action for each participant while reducing energy consumption and processing delay. The model is validated through four case studies, demonstrating an average improvement of 60% over existing methodologies. These findings highlight the effectiveness of integrating game theory with evolutionary optimization to enhance real-time healthcare monitoring.

Introduction

The monitoring of health in all individuals is a crucial aspect of society, as it facilitates the need for interconnectedness and effective roles in the monitoring process. Therefore, a novel framework for establishing real-time connectivity is employed, utilizing game theory to connect individuals as active participants, with all connected participants assuming the role of defenders. Furthermore, the integration of game theory can be applied to various Internet of Things (IoT) applications, as it assumes a pivotal role in contemporary healthcare monitoring systems. It is plausible that a significant portion of research is conducted within a cohesive paradigm, rendering it one of the most influential platforms to have emerged for healthcare applications. The healthcare monitoring system operates through a direct connection between specialists, end users, and other stakeholders, facilitating a two-way communication. However, the proposed method introduces a novel approach where four performers are chosen to engage in a game mode. Simultaneously, the health status of individuals is assessed and processed independently.

In the aforementioned connection process, in the event of an attacker, all connected entities have the ability to detect and protect themselves, thereby leading to the prevention of data loss and subsequent failure. Furthermore, game theory is employed to analyze the interaction between two separate Internet of Things (IoT) devices, with equilibrium conditions being established through the utilization of a deterministic model that is characterized by analytical equations. The implementation process leads to the maximization of utility functions, ensuring that the state of action for each performer remains favorable. Figure 1 provides the conceptual framework of game theory in health care monitoring systems. From Fig. 1 it is implied that four performers are connected with current network that provides seamless wireless and wired connectivity to all users in the connected game. The probability of available users are marked with probability symbols and it is directly connected to IoT networks therefore as a result the third performer in the group is monitored by specialists in first group of connected network. Once the corresponding performer is monitored then reports are monitored performer is transmitted to second performer and they are denoted as health clinics. At the same time the home users and other users involved as third and fourth performers can able to self-monitor them thereby remote solution is achieved.

Fig. 1

Connected game theory for healthcare monitoring system using IoT.

Research gap and motivation

Despite the utilization of sophisticated models for healthcare applications by certain researchers, there continues to be a lack of interconnectedness among users across various platforms. Furthermore, the delay in processing units will be increased in unconnected mode, which is undesirable considering the significant role that healthcare applications play in the general public monitoring system. Furthermore, the existing approaches fail to identify the performance of individuals that leads to failure in the monitoring process, whether it is due to specialist or data collecting personnel. The current methods for creating a smart processing identification system are inadequate due to the unique nature of various algorithms used in IoT procedures. Therefore, the method proposed in this study utilizes game theory as a means to address the aforementioned requirements.

RG1: To include various performers as defenders against various attackers in IoT process thereby determining the strategy of each performer.

RG2: To define the deterministic game theory in healthcare applications to make a four cycle process in order to connect four different entities.

RG3: To identify nodes and other reckoning functions thus minimizing the delay of data processing technique.

Major contributions

The primary objective of the proposed method is to incorporate a mathematical model using game theory which is integrated with two evolutionary algorithms in order to maximize of minimize the following parametric functions.

• To determine the state of action for every performer under two conditions for decision activities thereby maximizing the gain of each performer.

• To tune the performer using individual nodes thus maximizing the strategy of each performer by identifying different functions.

• To minimize the delay in data processing system using IoT where the energy of performers in connected game is maximized.

Paper organization

The subsequent sections of this paper are structured as follows: Sect. 2 describes the comparison of existing approach with proposed objective functions. Section 3 presents an analytical representation of game theory for the purpose of defining each participant in healthcare monitoring systems. Sections 4 and 5 elucidate the significance of integrating evolutionary algorithms within the realm of game theory to effectively monitor states. Section 6 presents the results of the combined system model in four distinct scenarios. In conclusion, Sect. 7 provides an overview of the paper’s findings and offers suggestions for future research endeavors.

Background and relevant works

This section presents a compilation of significant contributions made by multiple researchers, with the aim of examining the significance of the game theoretic approach in diverse applications of the Internet of Things (IoT). The majority of Internet of Things (IoT) applications are developed using analytical models that represent either probabilistic or deterministic characteristics. These models are used to facilitate continuous monitoring and contribute to the overall growth of IoT systems. The study conducted in¹ examines a comprehensive range of IoT applications to analyze the various design aspects from a game theoretical perspective. The implementation of IoT applications can be optimized by incorporating maximum utilization functions, allowing performers to execute individual actions while ensuring a high level of quality of service. However, it is necessary to represent the utilization function using selected game equilibrium conditions without altering the order of selection, as it is crucial to monitor the actions of every player. The food monitoring process, which involves the use of IoT applications, is subject to a dynamic task. In order to evaluate the quality of different food criteria, a game theoretic approach is employed². The food quality monitoring system described above is implemented in various food processing industries, where decision-making is conducted using a game theoretic approach. On the other hand, when it comes to altering food processing units, ensuring consistent measurement changes becomes significantly more intricate. Consequently, the game theoretic approach being considered must possess the ability to adapt to diverse conditions. Furthermore, in order to adapt to evolving circumstances, it is imperative to conduct a comprehensive investigation. Consequently, an efficient postponement strategy can be implemented, taking into account energy-efficient conditions, through the utilization of fog distributed systems³. As a result of alterations in environmental conditions, the fog monitoring system is capable of delivering outcomes with varying latency at multiple locations. This identical condition is also reflected through the utilization of remote cloud servers. When conducting experiments involving fog in a game theoretic framework, there is a potential increase in energy consumption ranging from 10 to 20%. It is crucial to either avoid or optimize this increase.

A similar application to behavior monitoring systems in the realm of IoT involves the analysis of socio-economic conditions⁴ through the utilization of a game theoretic approach. During this procedure, a behavioral learning methodology can be observed, and it is necessary to document the changes exhibited by each participant using a management algorithm. The integration of unique features is necessary in data transmission algorithms to effectively handle management algorithms in game theoretic algorithms, which pose challenges due to their probabilistic nature. Therefore, it is advisable to adhere to a boundary condition for each game theory analysis involving IoT transportation applications⁵. In transportation applications, it is customary to assess the rationality of drivers by examining the likelihood of any changes occurring. It is evident that in the field of game theory, it is imperative for every defender to be present in a state of non-change, thereby facilitating enhanced monitoring of the transportation of each participant. The effective management of security optimization techniques is crucial in game theoretical models to enhance the performance of IoT applications⁶. Therefore, a security model is devised for vehicular applications in game theory, wherein both transmitters and receivers are equipped with digital signal processors. If these processors are employed in the backend, they can effectively monitor the intensive activity of each system against multiple attackers, allowing the corresponding performer to carry out various actions without being disrupted by external factors. Moreover, a data trust model is proposed in the form of a bargain game model, incorporating a unique path following mechanism to identify each malicious node present in IoT processing systems⁷. The majority of bargaining models exclusively offer Pareto optimal solutions, making it challenging to discern the underlying bargaining patterns without considering individual decision-making processes.

Therefore, in order to enhance game theory in IoT applications, a multimode routing protocol is established, incorporating a probabilistic set to effectively connect two or more nodes at suitable locations⁸. In order to mitigate potential confusion during the connection process, a gateway is implemented to facilitate interconnection among a designated group of available performers. However, the establishment of interconnections within a heterogeneous Internet of Things (IoT) platform presents a significant challenge in configuring devices using game theory. The conversion of a challenging task into a simpler one is facilitated by the utilization of mathematical models that incorporate game theoretic representations. This approach is outlined in a study that proposes a mechanism based on a single performer strategy⁹. The game model described in the aforementioned case employs a conventional gaming procedure to identify each participant. This procedure necessitates the redefinition of equilibrium states within the system’s state representations. An alternative approach to redefining spatial considerations involves the utilization of game theory, which employs intermediate agents to facilitate a series of interaction processes. In this context, all agents within various application systems are able to engage in unrestricted interactions with one another¹⁰. In order for a given interaction process to proceed smoothly, it is imperative for the defender to establish a finite set of actions for the performers involved. This requirement poses challenges in the implementation of game theory. Furthermore, the execution of the specified set of actions can only be achieved if evolutionary algorithms are employed in a more comprehensive manner, as opposed to conventional processing segments. Table 1 presents a comprehensive comparison of contemporary methodologies that employ clearly defined objective functions.

Table 1 Existing vs. proposed.

Proposed system model

The successful operation of an Internet of Things (IoT) network for healthcare applications, based on game theory, requires the development of a robust working model that can be validated through the use of mathematical expressions and the establishment of interconnected relationships. Therefore, this section focuses on the development of the system model, which consists of four distinct performers interconnected in a circular manner to facilitate the execution of multiple actions. Furthermore, the primary rationale for selecting four performers in a health-based application is to mitigate the decline in performance of the interconnected Internet of Things (IoT) network. Each of the four players in the network is assigned a distinct time period of operation. Hence, following a designated duration, each person modifies their portrayal of activities through distinct action representations. Therefore, the Eq. (1)^17,18,19 presents the current state of action for all participants.

$$\:{players}_{i}=\sum \limits_{i=1}^{n}{[\tau\:}_{i}+{\tau\:}_{w}\left(i\right)]\times\:{b}_{t}$$

(1)

Where,

$\:{\tau\:}_{i}$, $\:{\tau\:}_{w}\left(i\right)$ represents delay and no delay conditions

$\:{b}_{t}$ denotes encouragement for decision activities

Proposition 1

Let us consider that {i, n} set of actions must be taken for each player by considering their corresponding activities and in this type of propositions the delay factors which are indicated by $\:{\tau\:}_{1}+.+{\tau\:}_{i}$ must be known. In case if the delay periods are reduced with respect to certain activities then propositions can be indicated using $\:{\tau\:}_{w}+.+{\tau\:}_{n}$. Hence for proving set of actions in each player distributive law is considered where indicative actions are measured.

Lemma 1

The set of actions are restated as follows,

$$\:{player}_{1}\in\:{\varrho\:}_{1}\nexists\:any\:other\:players$$

(2)

$$\:{player}_{i}\in\:{\varrho\:}_{i}\nexists\:any\:other\:players$$

(3)

The above set of players must follow the actions at reduced delay factors with certain subgroups but in intention of proposed method unequal conditions may also raise. Therefore the distributive theorem can be stated as,

$$\:{player}_{1}.{player}_{i}\exists\:{ld}_{1}.{ld}_{i}$$

(4)

Hence the low delay conditions exists for all players in particular group and at designated duration included four players can take appropriate actions. Equation (1) demonstrates that the completion of the state of action is necessary for all four players, regardless of the presence or absence of delays. Moreover, decision activities must be undertaken at each time period, accompanied by supportive reinforcements. In the context of interconnected Internet of Things (IoT) networks, it is conceivable that one or more entities may exhibit a state of inactivity, despite receiving encouragement or stimuli. Hence, in light of the aforementioned circumstance, the perpetrator will undergo evaluation utilizing Eq. (5) in the subsequent manner.

$$\:{G}_{i}=max\sum\limits_{i=1}^{n}{L}_{a}\times\:{u}_{i}$$

(5)

Where,

$\:{L}_{a}$ indicates total layers that are attacked by external performers

$\:{u}_{i}$ denotes convenience function for each performer

Proposition 2

The proposition for attack must be defined for certain players even if low delay conditions are present therefore in this case a non-logical classical functions must be defined by considering layers $\:{L}_{1}+.+{L}_{i}$ that are expressed in convenience to each player at rate of $\:{u}_{1}+.+{u}_{i}$ which can be identified by using intersection principle.

Lemma 2

The intersection rule that defines the layer attack of each player can be represented with function defined representations as indicated in Eqs. (6) and (7).

$$\:{IF}_{i}\notin\:{inter}_{i},{IF}_{i} \varsubsetneq {u}_{i}$$

(6)

$$\:{\otimes\:}_{g}\subset\:{A}_{d}\left(i\right)$$

(7)

For the aforementioned case the inflow data proportions must not intersect the players and convenience rate of each player. However if number of game processed by each player can be detected with respect to various attacks thus if configurations are equalized the intersection principle can be followed. According to Eq. (5), it is necessary to optimize the gain of each performer by avoiding the presence of external performers who are not registered users. The establishment of a controlled IoT network with data security measures can be achieved through the exclusion of external actors. The efficacy of game theory in IoT healthcare applications is contingent upon the distribution of performers with probability values. Therefore, if the performance of any individual is diminished, it is possible to devise a distinct approach by utilizing Eq. (8) as stated in¹⁸.

$$\:{ST}_{i}=max\sum\limits_{i=1}^{n}\frac{{t}_{i}\times\:{\alpha\:}_{in}}{{\delta\:}_{i}}$$

(8)

Where,

$\:{t}_{i}$ denotes tunable performer actions

$\:{\alpha\:}_{in}$ indicates probability of several occurring actions

$\:{\delta\:}_{i}$ determines the total probability of each performer

Proposition 3

The performance of each player must be distinguished in such a way by defining four steps in evaluation theorem where $\:{player}_{i} {\text{e}} {\mathcalligra{l}}_{i},{{\Sigma\:}}_{i},{\chi\:}_{i},{\mathfrak{L}}_{i}$. If each player in a group is distinctive representatives of selection, summation, calculation and inference then prediction mode will be activated with $\:{player}_{i}\subset\:{\odot}_{i}$.

Lemma 3

For each player within the represented dot circle the tunable actions can be proved and represented as,

$$\:{\kappa\:}_{i}\subset\:{t}_{i}\not\equiv\:{\kappa\:}_{i}\in\:{\delta\:}_{i}$$

(9)

At the identical actions the tunable representations can also be defined as,

$$\:{\psi\:}_{i} \leftrightarrow {\alpha\:}_{in}\subset\:{t}_{i}$$

(10)

The probability of unique representations which represents appropriate predictions are tuned with inference values thus actual persuasive players are known. Equation (8) is derived with the purpose of facilitating comprehensive control actions for diverse performers. It is imperative that each controlled action is communicated to adjacent performers to ensure the continuation of authorized usage. In IoT systems, data exchange among the four performers is facilitated through individual nodes. Consequently, the connectivity of nodes for all performers is denoted by source and destination points, which are defined using Eq. (11) as stated below.

$$\:{nodes}_{i}=\sum\limits_{i=1}^{n}({\omega\:}_{s}\to\:{\omega\:}_{d})\times\:({data}_{i}+{data}_{r})$$

(11)

Where,

$\:{\omega\:}_{s}$, $\:{\omega\:}_{d}$ indicates source and destination nodes

$\:{data}_{i}$, $\:{data}_{r}$ denotes initiated and concentrated data types

Proposition 4

Let us consider each player connectivity as with individual data as $\:{data}_{1}.{data}_{i}$ which indicates that network graph theorem must be considered thus achieving relevant mapping units with $\:{map}_{1}.{map}_{i}$. The connectivity network segments is a subset of two nodes {$\:{\omega\:}_{s},{\omega\:}_{d}$} thereby preventing failure of both source and destination which can later be discovered using other subset using $\:{\varsigma\:}_{i}\to\:{NH}_{i}$. Since non-hidden nodes are involved using discovery functions the identical theorem can be proved as follows.

Lemma 4

The own vertices network nodes can be represented with individual data as follows,

$$\:{\mathcal{B}}_{i} \iff \:{\mathcalligra{z}}_{in}\subset\:{\omega\:}_{s}\parallel\:{data}_{i}$$

(12)

The above equation indicates that for network player theorem the Bernoulli function with two node function must contain data in parallel representation hence flow of data will not be affected. In other case the parallel representation that is not a function of data unit can be represented as follows.

$$\:{\mathcal{F}}_{i}\iff {\text{{T}}}_{in}\nleqq\:{player}_{i}$$

(13)

Equation (11) stipulates that distinct data points are assigned to each source and destination node, enabling all actors to generate active data prior to the detection of any failure. In the context of an IoT healthcare monitoring system, it is imperative to have a designated individual who actively participates in data capturing. Consequently, it becomes crucial to monitor the energy status of the participants and the connectivity of data nodes by employing game theoretical Eq. 

$$\:{Energy}_{i}=max\sum\limits_{i=1}^{n}\varDelta\:({E}_{c}-{E}_{i})$$

(14)

Where,

$\:{E}_{c}$, $\:{E}_{i}$ denotes performer energies at current and initial states.

Proposition 5

Let the minimum amount of energy that is used for transmitting single bit of energy is $\:{energy}_{i}\succcurlyeq\:{CU}_{i}$ in such a way the launder limit must be maintained. Hence two terminals with data transmission and reception must be equalized in a form that is maintained with probabilities {i, j}.

Lemma 5

The launder limits for $\:{player}_{i}$ is represented using matrix representations that determines $\:{o}_{in}$ with high and low energy determinations. Thus the non-identical launder formula can be indicated as follows,

$$\:{{\Gamma\:}}_{i}\nrightarrow\:{{\Gamma\:}}_{c}\subset\:{energy}_{i}$$

(15)

Equation (14) establishes that the attainment of maximum energy is contingent upon the provision of the disparity between the present and initial states. In cases where low energy is indicated, the utilization of the reckoning function in game theory becomes necessary. In order to establish connectivity among various performers, it is necessary to provide a reckoning function along with a convenience function, as defined in Eq. (5). The reckoning function delineates the potential pathways through which individual performers may counteract a specific assailant by opting for alternative routes. Therefore, the establishment of route connectivity is achieved by utilizing Eq. (16) in the following manner.

$$\:{u}_{i}=max\sum\limits_{i=1}^{n}\left({Route}_{i}+{Route}_{n}\right),({Route}_{i}+{Route}_{j})$$

(16)

Where

$\:{Route}_{i}$, $\:{Route}_{j}$ and $\:{Route}_{n}$ determines separate route connections for preventing attackers

Equation (16) demonstrates the necessity of maximizing the class of routing functions by employing diverse routes. This approach enables the performer to effectively counteract potential attacks through the utilization of game-theoretic expressions. In the context of game models, it is imperative that each performer is promptly represented within the group. The absence of any delay signifies the efficient functioning of IoT devices, as they operate at high speeds, thereby mitigating idle operating conditions. Therefore, the game theoretic delay for each performer can be minimized by utilizing Eq. (17) in the following manner.

$$\:{delay}_{i}=min\sum\limits_{i=1}^{n}\frac{{\phi\:}_{p}+{\phi\:}_{i}}{{ST}_{d}}$$

(17)

Where,

$\:{\phi\:}_{p}$, $\:{\phi\:}_{i}$ denotes processed and idle data types

$\:{ST}_{d}$ represents speed of device performer

The reduction of delay in IoT health monitoring systems is achieved through the identification of the idle performer in the system, as determined by Eq. (17). Increasing the speed of operation is feasible by removing a greater number of idle performers. The proposed methodology formulates the objective functions within a multi-objective framework, allowing for the representation of a min-max function. Therefore, by integrating all the presented formulations, the individual objective function for the game model in IoT healthcare can be determined as follows.

$$\:{obj}_{1}=max\sum\limits_{i=1}^{n}{G}_{i},{ST}_{i},{Energy}_{i}$$

(18)

$$\:{obj}_{2}=min\sum\limits_{i=1}^{n}{delay}_{i}$$

(19)

The aforementioned equations pertain to the optimization of various parameters that are directly associated with game models, with the aim of maximizing or minimizing them. Therefore, it is imperative to enhance the efficacy of the optimization process through the identification of algorithmic flow accompanied by clearly defined objectives.

Methods and materials

A game theoretic model has been developed to reduce the operational capabilities of individuals. To achieve this, an integration of an Artificial Intelligence based Evolutionary Algorithm (AIEA) is necessary. The AIEA will facilitate the reproduction of performers with new actions, enable performers to execute intelligent actions, and configure each performer based on the specified application. The primary significance of employing evolutionary algorithms in game theoretic models lies in their ability to discern the stochastic attributes exhibited by each participating agent. Hence, once the stochastic characteristics have been identified, it becomes possible to observe the uncertainty in each data operation without the interference of noise. Even with an increase in the number of performers, it is feasible to adjust to evolving circumstances, thereby enabling the attainment of optimal solutions without any delay. Furthermore, an alternative approach can be proposed for the game theoretic model by expanding the scope of each participant to generate novel solutions within the interconnected systems¹⁹. Game theoretic problems are typically formulated using non-linear representations. By doing so, the size of the problem can be determined. If the problem size is increased, it is possible to either reduce the cost functions or keep them constant. Moreover, the AIEA exhibits a high degree of resilience when it comes to discerning the health conditions of diverse individuals and performers^{20,21,22,23,24,25,26,27}. Consequently, a clear-cut determination can be reached for all performers within a game-theoretic framework. The determination of recital activities for each performer can be achieved by employing previous instances of identification cases, wherein a localized search technique is employed for each interconnected performer. The mathematical formulation of AIEA, utilizing a game theoretic framework, can be expressed by combining the various analytical representations in the following manner. The selection of individual performers in healthcare applications through the utilization of a game theoretical model is contingent upon the fluctuation of probability values in accordance with temporal factors. Therefore, Eq. (20) is formulated as follows.

$$\:{\rho\:}_{i}=\sum\limits_{i=1}^{n}z({P}_{1}+.+{P}_{4})\times\:{time}_{i+1}$$

(20)

Where,

$\:{P}_{1}+.+{P}_{4}$ indicates four performers

$\:{time}_{i+1}$ denotes next changing time periods

Equation (10) depicts the temporal dynamics of the four performer actions, wherein any instances of similar performers occurring within the same time period are eliminated from the interconnected game systems. In the context of game theory, it is feasible for a player to form alliances with other players through the utilization of an applied selection technique. This technique is represented by the utilization of probable values, as denoted by Eq. (21).

$$\:{combination}_{i}=\sum \limits _{i=1}^{n}{(\vartheta\:}_{P1}+{\vartheta\:}_{P2})+.+{(\vartheta\:}_{P4}+{\vartheta\:}_{P1})$$

(21)

Where,

$\:{\vartheta\:}_{P1}+{\vartheta\:}_{P2}$ denotes combination of first and second performer

Equation (21) indicates that combination of performers is extended and once all performers are combined then parameters for each combination are provided based on individual characteristics. In the context of game theory, it is necessary for a performer to possess a transfiguration technique that can be employed in the event of failure, with the intention of utilizing it at a subsequent stage. Therefore, Eq. (22) is derived by incorporating the mutation constraint.

$$\:{TCF}_{i}=\sum\limits_{i=1}^{n}{MU}_{i}\left({\vartheta\:}_{P1}-{\vartheta\:}_{P2}\right)+.+{(\vartheta\:}_{P4}-{\vartheta\:}_{P1})$$

(22)

Where,

$\:{MU}_{i}$ denotes total transmuted function between two independent performers

Equation (22) delineates the capacity of a game theoretic model to diminish the transmuted function by quantifying the disparity between two performers. This mechanism serves to deter unidentified assailants within the system. The flow of AIEA is facilitated through the utilization of the loop formation technique, as depicted in Figs. 2 and 3, which presents the block representations.

Algorithm

AIEA.

Evolution strategy

While evolutionary algorithms demonstrate improved performance in a game theoretic framework, it is crucial to adhere to a natural strategy for selecting diverse individuals that dynamically adapts over time. The efficacy of evolutionary strategy hinges upon the evaluation of each individual solution’s capacity to perform a range of actions associated with health applications^22,23. The strategy of representations is implemented by minimizing the number of transfigurations, thereby ensuring that performers of the same type are never formed within the connected group. In contrast to AIEA, the Artificial Intelligence based Evolutionary Strategy (AIES) employs a game theoretic approach that enables it to dynamically adjust to various evolving characteristics, contingent upon the types of decision variables involved. Therefore, the AIES is capable of conducting both direct search and optimization-based search without taking into account the recombination factor. The utilization of a direct search optimization technique enables the efficient definition of the search space for individual performers within a brief timeframe, thereby facilitating the attainment of optimal self-adaptation types. The primary strategy employed in AIES involves maintaining a constant number of performers²⁴. If any modifications are made using a game theoretic approach, the deterministic method of identifying performers is altered to encompass the entire population of performers. It is imperative to refrain from implementing the aforementioned manual alterations in the game theoretic framework for healthcare applications, as the task of determining the population of each participant becomes significantly intricate without conducting a thorough analysis of their fundamental attributes. Each performer must be provided with an individual argument function for the optimization function, which will utilize measurements obtained from connected sensing modules. Therefore, the optimization function can be formally defined utilizing Eq. (23) in the following manner.

Fig. 2

Block representation of AIEA in game theoretic approach.

Fig. 3

Flow of AIEA with variations in performers.

$$\:{k}_{i}=\overline{argopt}\sum\limits_{i=1}^{n}f\left(k\right)$$

(23)

Where,

$\:f\left(k\right)$ indicates total functionality representations for selected performer

Equation (23) delineates the necessity for the argument function to be formulated as an optimization strategy that must be adhered to by all participants. When considering the execution of each individual act by performers, it is necessary to improve any adapted strategy that is being followed in order to select the most skilled performer within the associated group. The primary rationale behind choosing the most accomplished individual is to facilitate the training of the subsequent cohort, particularly in areas where the integration of various functions is discerned. Hence, the optimal performer in this scenario can be determined by utilizing Eq. (24) in the following manner.

$$\:{BP}_{i}=\sum\limits_{i=1}^{n}\left({{\aleph\:}}_{i}+1\right),({{\aleph\:}}_{i}-1)$$

(24)

Where,

$\:{\aleph\:}_{i}$ denotes number of mixing features with descendants

Equation (24) describes that every mixing feature must be accompanied using two sets that contains positive and negative value functions with constraint representation as follows.

Algorithm

AIES.

The selection strategy employed by each performer is contingent upon the ranking of the selection, thus resulting in the use of a strategy constraint to determine the individual selection, as denoted by Eq. (25).

$$\:{\complement\:}_{i}=\left\{\begin{array}{ll}{{\aleph\:}}_{i} & \quad if \; f\left(k\right)<1\\\:0 & \quad otherwise\end{array}\:\right.$$

(25)

The constraint represented by Eq. (25) indicates that individual termination of a performer occurs when unusual activities are detected during the selection rankings process. The flow of the Artificial Intelligence Expert System (AIES) is facilitated through the utilization of the loop formation technique, as depicted in Figs. 4 and 5, which illustrates the block representations.

Fig. 4

Block representation of AIES in game theoretic approach.

Results

This section focuses on the analysis of real-time experimentation outcomes in the context of game theory. It involves the utilization of probabilistic equations and evolutionary optimization scenarios. The examination is conducted in a flexible manner as the entire process utilizes software-defined radio, wherein all hardware components are interconnected in a software-equivalent manner. Furthermore, the utilization of a game theoretic approach in conjunction with software modules allows for the efficient reuse of these modules. This approach also facilitates a streamlined testing and design process, wherein individual components can be easily detached and interconnected. In order to conduct real-time experimentation on game theory, the study involves four performers situated at distinct locations. The entirety of the data set is provided as input, comprising textual information and visual representations. The image set encompasses various types of infections, enabling specialists to conduct a comparative analysis to ascertain the prevalence rates across different regions.

Fig. 5

Flow of AIES with limited performers.

In the context of various syndromes, an individual designated as performer 1 makes a determination to generate a comprehensive report pertaining to an associated patient. This task is facilitated through the utilization of a cloud storage system. Furthermore, the significance of the state of action for each individual user is prominent within the report center, enabling decision-making activities to be conducted at any given point in time. Furthermore, a distinct strategy is implemented for each affiliated participant, as numerous tasks necessitate prompt completion. Moreover, the evolutionary optimization technique utilizing the Adaptive Individual Evaluation Algorithm (AIEA) and the Adaptive Individual Selection Algorithm (AIES) is employed to select the optimal combination of performers. This process determines the most proficient performer at each stage, ensuring the continuity of connections with the same users in the interconnected game. Furthermore, within the realm of connected game theory, the identification of the conqueror remains indeterminate, as the sole activity undertaken between each participant is the processing of data. To examine the parametric outcomes of each performer, a series of case studies were conducted. The significance of these case studies is outlined in Table 2.

Case study 1: State of action and gain.

Case study 2: Strategy of performers.

Case study 3: Energy and reckoning functions.

Case study 4: Performers delay.

Table 2 Importance of case studies.

Discussions

All of the aforementioned case studies were conducted using AIEA and AIES methodologies. Consequently, a comparative analysis was conducted to determine the most effective optimization approach, thereby enabling the selection of optimal solutions. In order to observe the outcomes in case studies, a graph-based model is employed in MATLAB. This approach allows for a comprehensive analysis of the various states of actions chosen by individual performers, thereby providing a clear indication of the observed results. In the initial state, it is observed that individuals perceive the need to engage in a connected game by utilizing the shortest path in the network. Subsequently, the choice of individual paths to follow is contingent upon their decision-making process. The environments necessary for conducting simulation analysis are presented in Table 3.

Table 3 Simulation parameters.

The simulation parameters are distributed as a unified package to all users, thus the selection of gambit optimization is made for the purpose of conducting integrated operations involving AIEA, AIES, and the proposed system model. The subsequent section provides a comprehensive overview of case studies.

Case study 1: state of action and gain

When making significant decisions, it is necessary to evaluate the potential outcomes of two scenarios: one where there is a delay in taking action, and another where there is no delay. The connected game provides the state of actions for all four performers, enabling the checking of the report and subsequent actions. This ensures that every health monitoring system yields positive outcomes. When the state of actions for connected users is deemed suitable, the maximization of gain occurs, and the measurements of gain are conducted by replicating both external attacks and convenience functions. In the event that a greater number of attackers are present, it is imperative that each connected performer adopts a distinct course of action, thus enabling the implementation of an effective defensive strategy. If performer 1 fails to take appropriate action, the other performers will be adversely affected, as performer 1 is designated as the decisive specialist in the interconnected game. The simulation analysis in Fig. 6 presents the gain measurements after taking into account the relevant state of actions.

Fig. 6

Percentage of gain according to state of action.

Table 4 Gain for game theoretic approach with action representations.

From Fig. 6; Table 4 it is obvious that gain for all connected performers in game theory is maximized in case of proposed method as compared to existing approach. To verify this case study the delay and no delay representations are made where delay is present at negligible amount. Therefore at no delay conditions the decisive actions are replicated and it is indicated as connected state of action between four performers. To conduct the experimental case study out of four layers a consideration is made from 1 to 4 which indicates that all layers with connected performers are attacked. For the above mentioned attacks all the four defenders chooses the state of actions with a total percentage of 52,79,83,89 and 94 where corresponding actions are maximized if all performers are attacked. With proper state of actions the proposed method maximizes the performer gain to 99% in case of projected model whereas existing method¹² provides performer gain for about 75%. Hence with proposed game theory in both AIEA and AIES the gain is maximized in case of proposed method.

Case study 2: strategy of performers

In the field of game theory, it is necessary for each participant to adopt a distinct strategy, as the computational process of making decisions relies entirely on adhering to strategies that are pertinent to various actions that arise. If the strategy of each performer is appropriately calibrated, it becomes feasible to consistently execute the same strategy until decisions are reached. The strategy employed by each performer is examined by replicating both adjustable actions and potential decisions, which are then categorized by the total number of actions. In the proposed method, the strategies of performers 1 and 2 are initially identical during the first state of operation. Combinations are selected in a similar manner, and are subsequently modified to a certain extent as the combination changes. Furthermore, the composition of each performer undergoes alterations at different intervals, thereby facilitating the implementation of defensive measures against potential assailants. If there is an unexpected change in the combination of performers, it is necessary to notify performer 1, as the entire game is dependent on their involvement. Figure 7 displays the results of the simulation in terms of the percentage of accurate strategies.

Table 5 Maintenance of correct strategies for considered actions.

From Fig. 7; Table 5 it is realistic that strategy on taking correct decisions is maximized in projected model as compared to existing approach¹². Whenever a new performer is present in the system then strategy of existing user remains in protected mode therefore even if unknown users enters into the system then strategy of other users remains unaffected. To verify this case study number of performance from four users that is tuned for various point remains at 8,12,15,19 and 22 with total number of modified actions as 3,5,8,12 and 14 respectively. Hence for each tuned actions percentage of correct strategy is measured and in proposed method more number of times correct strategies are provided. This can be proved with number of tunable performance and total actions with 22 and 14 where percentage of correct strategy in this case is 94 for projected game theory model and 78 for existing approach. Hence with increased gain the strategy followed by each user remains at safe position.

Fig. 7

Correct strategies of performers with tunable characteristics.

Case study 3: energy and reckoning functions

By manipulating the data connection pathways, it becomes feasible to establish a connection between each performer and the calculation functions, thus enabling the creation of representations for game systems with multiple routes. In this process, the performers strive to maximize their energy, thereby prompting them to adopt various routes in order to execute decisive actions. The energy representation of each performer is assessed by calculating the discrepancy between the initial and final states of their representations, taking into account the varying node function at each point. Therefore, the present energy level is assessed at each node, allowing the performer to establish connections by employing a strategic approach that is independent of potential attackers, as the energy levels of performers are not predetermined in their current positions. Furthermore, in the event that the energy level of performers is diminished, it may result in the disconnection of other users. As a potential alternative solution, a three-player representation could be implemented. Figure 8; Table 6 illustrates the energy and reckoning functions, along with the corresponding simulation outcomes.

Table 6 Route indications for data processing at varying energy rates.

Fig. 8

Stacked route representation with maximized energies.

From Fig. 8; Table 6 it is obvious that energy and reckoning functions are maximized for proposed method as compared to existing approach¹². As more number of routes is chosen in the game for analyzing the health of individuals it is not possible for the attacker to determine exact reckoning functions and if any failure happens then it will be indicated. To verify the energy representation and reckoning function total amount of energy is chosen as 100,200,300,400 and 500 where reckoning functions at initial states are represented with 3 different routes. Later it is realized that some of the performers are not organized in a particular way due to more number of connections. Hence all interrupted connections are found and a new route is established thereby preventing every performer from attackers. As a result of such activities entire health record is maintained and the number of routes followed in the proposed method is maximized to 81% whereas in existing approach it is maintained at 54%.

Case study 4: performers delay

In order to facilitate efficient decision-making systems in game theory, it is imperative to address the inherent delay that arises from the interconnectedness of users. Minimizing this delay is crucial for the optimization of intelligent healthcare operations. Therefore, in this particular scenario, a delay in performance is observed for all connected defenders. Furthermore, it is important to consider the potential for delays in the event that another performer disrupts the connected system. This can result in a total delay, particularly when data remains in an idle state during the interruption. In the proposed methodology, delay is quantified by incorporating two distinct data types, which segregate the device performer from the connected performers. This differentiation allows for the processing of individual data by the connected performers, which deviates from conventional data operations. If the delay period exceeds a certain threshold, the connected performer will be indicated as experiencing a timeout and will be offered the option to reconnect at a later stage. The outcomes of delay for four connected performers are presented in Fig. 9.

From Fig. 9; Table 7 it is realistic that performer delay is reduced for proposed method as compared to existing approach¹². To prove the minimization factor idle type connections are processed with separate channel and known performers are connected. To verify this case study four performers as connected in health care system such as specialists, clinicians, monitoring patient and other individuals corresponding to monitoring patients are chosen thereby external delay is not present. With the considered individuals it is observed that number of idle devices remains at 7,11,14 and 16 thereby total amount of delay in proposed method is less than 1 s and in existing method the delay is greater than 2 s. In the process of game theory if more delay is present then there is a high chance of making the external individuals to get interrupted in the existing connections. Hence the proposed method operates with less delay when proposed game theory model is integrated with AIEA and AIES.

Fig. 9

Grouped idle devices for monitoring delay with connected performers.

Table 7 Total delay for idle device connections.

Performance measurements

The performance outcomes of evolutionary optimizations are evaluated by considering three specific features. These qualities are thoroughly analyzed to demonstrate the reliability of the game-theoretic approach. Furthermore, the combined optimization process demonstrates that it is possible to decrease complexity in terms of both time and space. The ability to consistently maintain accurate tactics at regular intervals offers a helpful approach to all aspects of game theory.

Time complexity

The time complexity of both the proposed and existing methods is shown in Table 8; Fig. 10 where it changes depending on the best epoch in the sets of {10,20}, {30,40}, {50,60}, {70,80}, and {90,100}. The difficulty of the described epoch periods is determined by quantifying the overall time period relative to the total number of considered routes. The time complexity of the present approach, after computation, is found to be 2.1, 1.8, 1.7, 1.5, and 1.3 s, respectively. In contrast, the total time complexity of the suggested method is 1.3, 1, 0.7, 0.4, and 0.2 s, respectively. The performance outcomes of evolutionary optimizations are evaluated by examining three specific qualities. These characteristics are thoroughly analyzed to demonstrate the reliability of the game-theoretic approach. Furthermore, the performance of the combined optimization process demonstrates the potential to decrease complexities in terms of both time and space. The ability to consistently maintain optimal strategies at fixed intervals offers a helpful approach to all aspects of game theory.

Table 8 Time complexity after quantifications.

Fig. 10

Execution of time complexities for best epoch.

Space complexity

To evaluate individual performance given the larger number of participants in the game theoretic method, it is crucial to determine the percentage of space each user occupies. Therefore, the total number of iterations has been increased from 10 to 100, taking into account the input values in relation to the decisions. The conventional methodology requires 20%, 17%, 14%, 11%, 9%, 8%, 6%, 5%, 3%, and 2% of memory space for the given iterations. In contrast, the proposed method uses 12%, 10%, 7%, 4%, 3%, 2%, 1%, 0.7%, 0.4%, and 0.2% of memory space for the same iterations as the number of users increases. The above mentioned variations are indicated in Table 9; Fig. 11.

Table 9 Memory capacities for changing iterations.

Fig. 11

Total memory space requirements with varying iterations.

Convergence rate

As stated in Case Study 2, the accuracy of the strategy remains consistent for all users. It is important to achieve convergence whenever possible. Therefore, this performance metric focuses on observing the rate of convergence. In order to measure the convergence rate, the most optimal epoch periods are identified as 10, 30, 50, 70, and 100. However, it is seen that the current technique fails to achieve satisfactory convergence at all these periods due to the lack of adequate strategies when the number of users is increased. However, the suggested method achieves convergence at the 50th iteration, consistently selecting the proper strategies with an accuracy of 94%. The above mentioned variations are indicated in Table 10; Fig. 12.

Table 10 Comparison of convergence rate for existing and proposed method.

Fig. 12

Comparison of convergence rate for correct decisions.

Conclusions

In the proposed method a game theory procedure is followed with four performers for monitoring the health condition of a particular individual. The analysis is made with four performers in order to maintain a strong defense strategy against different attackers hence every performer follows a unique state of action. As state of actions is maintained in the consecutive phases the strategies are completely different for all performers thereby maximizing the output gain in the monitoring process. Further the combination of performers in the connected system is much important in game theory which is formed by using evolutionary optimizations that includes AIEA and AIES. If the number of combinations is correct then it is possible to choose the best performer in order for enduring transfiguration between individual users. Moreover with IoT it is possible to choose a desired route for playing the connected game with separate nodes therefore performers are selected within the corresponding time period by following unique routes. In the combined system model with evolutionary optimization it is observed that high efficiency is achieved for game theoretic approach as route connectivity for performers is maintained in a better way. Further the outcomes of combined system model is provided with experimental analysis in a better way with comparison of AIEA and AIES. To perform real time experimentation four distinct case studies that represents the state of action, gain, strategies of performers, variations in energy, reckoning functions and delay periods are chosen and a pareto optimal representation is provided. From the compared outcomes it is realistic that proposed game theory with AIEA and AIES performs in a better way where gain is maximized to 99% and the delay in each performer is reduced below 1 s.

Limitations

While the proposed game-theoretic healthcare monitoring system enhances decision-making and security, further exploration is needed to adapt it to more complex and large-scale healthcare networks. The framework’s effectiveness in diverse real-world settings depends on addressing challenges related to data privacy, interoperability, and system scalability. Additionally, ensuring seamless energy efficiency across various IoT devices remains an area for future refinement. As healthcare environments continuously evolve, integrating adaptive and dynamic models will be crucial for broader applicability and long-term sustainability.

Future scope

Future research should focus on deeper integration with IoT technologies to enhance scalability, efficiency, and automation in healthcare monitoring. Incorporating edge and fog computing can minimize latency, while blockchain technology ensures secure and tamper-proof patient records. Additionally, AI-driven optimization can improve decision-making, and energy-efficient IoT sensors can extend device longevity. The convergence of 5G and IoT will further enhance real-time data transmission, enabling seamless and intelligent healthcare systems. Table 11 gives the list of abbreviations used.

Table 11 List of abbreviations.