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This study proposed a two-stage dual-game model methodology to evaluate the existing difficulty of healthcare accessibility in China. First, we analyzed a multi-player El Farol bar game with incomplete information by mixed strategy to explore the Nash equilibrium, and then a weighted El Farol bar game was discussed to identify the existence of a contradiction between supply and demand sides in a tertiary hospital. Second, the overall payoff based on healthcare quality was calculated. In terms of the probability of medical experience reaching that expected level, residents are not optimistic about going to the hospital, and the longer the observation period is, the more pronounced this trend becomes. By adjusting the threshold value to observe the change in the probability of being able to obtain the expected medical experience, it is found that the median number of hospital visits is a key parameter. Going to the hospital did bring benefits to people with consideration of the payoffs, while the benefits varied significantly with the observation period among different months. This study is recommended as a new method and approach to quantitatively assess the tense relationship in access to medical care between the demand and supply sides and a foundation for policy and practice improvements to ensure the efficient delivery of healthcare., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Wang, Weng, Chen and Zhu.)

In this paper, two kinds of distributed Nash equilibrium seeking strategies based on Kalman filter are proposed in non-cooperative games with incomplete information. In the discrete-time system with process and measurement noises, each player, selfish and only considering its own profit, utilizes the gradient method to maximize the benefit. Since the payoff function is related to all players' states, Kalman filter and leader-following consensus are used to estimate the states in the network. Furthermore, considering the trade-off between strategy precision of Nash equilibrium and communication rate, another Nash equilibrium seeking method is proposed by introducing an event-based scheduler. The convergence of both Nash equilibrium seeking strategies is analyzed based on Lyapunov method. It is proved that both strategies are bounded in the mean square sense. Simulation examples are given to verify the efficiency., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 ISA. Published by Elsevier Ltd. All rights reserved.)

The proposed model determines the allocation of security forces in response to terrorist events with a series of coordinated attacks such as the Paris terror attacks in 2015. Two games are constructed, representing the two stages needed for the rapid deployment of security forces. The first stage applies a firearms assault game to analyze the interaction behaviors between the response agent (or security force commander) and the attackers in each response district. The terrorist threat value (TV) during a firearms assault event can then be derived from the mixed strategy Nash equilibrium. The TVs are input to the second stage for computing the Shapley value for each event, in terms of the majority of TVs of all firearms assaults. The Shapley values are then used to create a set for reallocation of the limited security forces to respond to the multiple firearms assaults. The experimental results show the proposed division to fairer than the proportional division for allocating security forces., (Copyright © 2021 Elsevier Inc. All rights reserved.)

We consider a game theoretical model of kleptoparasitic interaction between two individuals, the Owner and the Intruder. The Owner is in possession of a resource and must decide whether to defend the resource against the Intruder or flee. If the Owner defends, the Intruder must decide whether to fight with the Owner or flee. The outcome of the fight depends on the hunger of the individuals, the hungrier the individual is, the more likely they are to win the fight. We consider three scenarios: (a) both individuals know their own and their opponent's hunger, (b) individuals only know their own hunger but not that of their opponent, and (c) individuals do not know their own nor the opponent's hunger levels. We determine Nash equilibrium strategies in each scenario. We conclude that Owner is generally willing to defend more often than the Intruder is willing to attack. Also, the Intruder's payoff is largest in the full information case; but the Owner may benefit in the no information or partial information cases when the cost of the fight is neither too large nor too small., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier Inc. All rights reserved.)

Hepatitis B (HepB) is one of the most common infectious diseases affecting over two billion people worldwide. About one third of all HepB cases are in China. In recent years, China made significant efforts to implement a nationwide HepB vaccination program and reduced the number of unvaccinated infants from 30 to 10%. However, many individuals still remain unprotected, particularly those born before 2003. Consequently, a catch-up retroactive vaccination is an important and potentially cost-effective way to reduce HepB prevalence. In this paper, we analyze a game theoretical model of HepB dynamics that incorporates government-provided vaccination at birth coupled with voluntary retroactive vaccinations. Given the uncertainty about the long-term efficacy of the HepB vaccinations, we study several scenarios. When the waning rate is relatively high, we show that this retroactive vaccination should be a necessary component of any HepB eradication effort. When the vaccine offers long-lasting protection, the voluntary retroactive vaccination brings the disease incidence to sufficiently low levels. Also, we find that the optimal vaccination rates are almost independent of the vaccination coverage at birth. Moreover, it is in an individual's self-interest to vaccinate (and potentially re-vaccinate) at a rate just slightly above the vaccine waning rate.

An efficient police patrol schedule must ensure the allocation of an appropriate number of officers sufficient to respond to the danger of criminal incidents, particularly in an urban environment, even when the available number of personnel is limited. This study proposes a framework that incorporates two game theory models designed for the allocation of police officers to patrol shifts. In the first step, the interactions of three factors between the criminal and the operation captain are modeled as a zero-sum, noncooperative game, after which a mixed strategy Nash equilibrium method is used to derive the risk value for each district to be patrolled. In the second step, the risk values are used to compute the Shapley value for all 10 districts, for three different threat levels. A fair allocation of police personnel based on the Shapley value is made with a minimum set of personnel deployment costs. The efficacy of the proposed method is verified using openly available data from the San Francisco City Police detailing incidents from the year 2016. The experimental results show that police planners can use this framework to quantitatively evaluate the criminal threat in each district when deciding upon the deployment of patrol officers for three shifts per day., (© 2019 Society for Risk Analysis.)

The authors apply the game theory principal agent model in which the principal is a donor who seeks to reduce or sequester harmful emission through a system of conditional payments, whereas the agent is a village community. The purpose is to explore strategic interactions between the two actors in the case of Mlumbilo village in Tanzania. Whereas carbon sequestration at minimum cost is an objective for the principal, the village community aims at maximizing the net present value of income from all types of land use. The application of both a multi-objective bio-economic model with detailed biological data and a bargaining game theory model with asymmetric information revealed that the choice of reference level used as a performance benchmark had major implications for the negotiated prices for CO 2 . However, the choice of reference level did not affect the cost efficiency of carbon sequestration. Additionally, the outcome of the bargaining model was unique and efficient. The authors conclude that recipient discretion will yield efficient results when the agent trusts that the principal will pay for verified sequestration., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

The current early-warning system and tsunami protection measures tend to fall short because they always underestimate the level of destruction, and it is difficult to predict the level of damage by a devastating tsunami on uncertain targets. As we know, the key to minimizing the total number of fatalities after a disaster is the deployment of search and rescue efforts in the first few hours. However, the resources available to the affected districts for emergency response may be limited. This study proposes two game theoretic models that are designed for search-and-rescue resource allocation. First, the interactions between a compounded disaster and a response agent in the affected district are modelled as a non-cooperative game, after which the risk value is derived for each district from the Nash equilibrium. The risk value represents the threat, vulnerability, and consequence of a specific disaster for the affected district. Second, the risk values for fifteen districts are collected for calculation of each district's Shapley value. Then an acceptable plan for resource deployment among all districts is made based on their expected marginal contribution. The model is verified in a simulation based upon 2011 tsunami data. The experimental results show the proposed approach to be more efficient than the proportional division of rescue resources, for dealing with compounded disaster, and is feasible as a method for planning the mobilization of resources and to improve relief efforts against devastating tsunamis., (Copyright © 2017 Elsevier Inc. All rights reserved.)

Cooperation in a public goods game has been studied extensively to find the conditions for sustaining the commons, yet the effect of asymmetry between agents has been explored very little. Here we study a game theoretic model of cooperation for pest control among farmers. In our simple model, each farmer has a paddy of the same size arranged adjacently on a line. A pest outbreak occurs at an abandoned paddy at one end of the line, directly threatening the frontier farmer adjacent to it. Each farmer pays a cost of his or her choice to an agricultural collective, and the total sum held by the collective is used for pest control, with success probability increasing with the sum. Because the farmers' incentives depend on their distance from the pest outbreak, our model is an asymmetric public goods game. We derive each farmer's cost strategy at the Nash equilibrium. We find that asymmetry among farmers leads to a few unexpected outcomes. The individual costs at the equilibrium do not necessarily increase with how much the future is valued but rather show threshold behavior. Moreover, an increase in the number of farmers can sometimes paradoxically undermine pest prevention. A comparison with a symmetric public goods game model reveals that the farmer at the greatest risk pays a disproportionate amount of cost in the asymmetric game, making the use of agricultural lands less sustainable., (Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The replicator equation is the first and most important game dynamics studied in connection with evolutionary game theory. It was originally developed for symmetric games with finitely many strategies. Properties of these dynamics are briefly summarized for this case, including the convergence to and stability of the Nash equilibria and evolutionarily stable strategies. The theory is then extended to other game dynamics for symmetric games (e.g., the best response dynamics and adaptive dynamics) and illustrated by examples taken from the literature. It is also extended to multiplayer, population, and asymmetric games.

The obstacle avoidance problem in geographic forwarding is an important issue for location-based routing in wireless sensor networks. The presence of an obstacle leads to several geographic routing problems such as excessive energy consumption and data congestion. Obstacles are hard to avoid in realistic environments. To bypass obstacles, most routing protocols tend to forward packets along the obstacle boundaries. This leads to a situation where the nodes at the boundaries exhaust their energy rapidly and the obstacle area is diffused. In this paper, we introduce a novel routing algorithm to solve the obstacle problem in wireless sensor networks based on a game-theory model. Our algorithm forms a concave region that cannot forward packets to achieve the aim of improving the transmission success rate and decreasing packet transmission delays. We consider the residual energy, out-degree and forwarding angle to determine the forwarding probability and payoff function of forwarding candidates. This achieves the aim of load balance and reduces network energy consumption. Simulation results show that based on the average delivery delay, energy consumption and packet delivery ratio performances our protocol is superior to other traditional schemes.

The emergence of blockchain creates a new possibility to solve the fraudulent problem of financial supply chain. We construct a game model to verify the strategic choice of the financial supply chain in an uncertain environment. We derive the equilibrium results and investigate the strategic choice of blockchain service for the financial supply chain. We also study the product price, product quantity, financing interest rate, and supply chain risk transmission, respectively. Specifically, when the blockchain is not considered, the financial model of supply chain led by core enterprises depends on firms' reputation. The retail and wholesale prices increase when fraud occurs or consideration payment increases. Besides, the market stability reduces price performance. In the blockchain environment, the strategic choices are divided into two cases: when choosing the core enterprise model and the third-party service model, the third-party service model is the equilibrium strategy; when choosing the third-party service model and the platform model, the platform model is the equilibrium strategy. [ABSTRACT FROM AUTHOR]

This article captures the effects of technology diffusion on innovation under duopoly competition. With the game theory approach, some interesting results are achieved. First, technology diffusion stimulates innovation and firms launch innovation to share more market size. Second, firms under unilateral innovation launch less innovation than that under bilateral innovation. Finally, neither firms' innovation constitutes a Nash equilibrium and subsidy may transfer this equilibrium to a new equilibrium that both firms innovate. [ABSTRACT FROM AUTHOR]

The connection between Average Daily Rate (ADR) and hotel room standard in both suburban and resort settings during high and low seasons remains an ongoing challenge. The purpose of this study is to craft practical cues for hotel managers to lean towards specific guiding cues for their effective decision-making of room rates. A study conducted on ADRs and guest comments from suburban and resort hotels across the United States from 2018 to 2023 utilized data from Smith Travel Research and TripAdvisor. Employing a vector error correction model and incorporating game theory, the research revealed that room standards are optimized in both types of accommodations when ADRs increase in resorts and decrease in suburban areas during peak seasons. [ABSTRACT FROM AUTHOR]

Security challenges in complex information technologies continue to grow and diversify. To improve network security, many researchers have explored the game theoretic approach as a hopeful modeling tool. Knowing that the attacker can take advantage of vulnerabilities and explore existing weaknesses in the network configuration to gain access to the system for a successful attack, our objective is to benefit from virtual machines' migration as a moving target defense technique and honeypot as a deceiving technique to increase the attack surface's dynamicity. This paper presents a game-theoretic framework for modeling attack-defense interaction. A model based on incomplete information game and attack graph is developed. Our main findings reveal in which case migration of virtual machines should be established in a architecture where a honeypot is deployed and identify the potential attack paths based on system security parameters. This provides network administrators with the ability to find unsecure nodes, avoid negative externality and more precisely inefficient migrations which impact the quality of service. [ABSTRACT FROM AUTHOR]

This study introduces a novel game-theoretic methodology to enhancing the optimization of Anti-Epileptic Drug (AED) selection for patients diagnosed with Juvenile Myoclonic Epilepsy (JME). The primary motivation is the need to enhance the treatment of JME by leveraging game theory principles to make informed decisions about AEDs. Within this framework, a novel cooperative Nash-based game model is proposed within the medical domain. It focuses on patients utilizing two distinct types of ADEs: Valproate (VPA) and Lamotrigine (LTG) to manage seizures while minimizing overall medical and non-medical expenses. The innovation lies in formulating a dynamic decision-making framework that integrates the patient's medical treatment selection, offering a unique Nash equilibrium decision under certain conditions. This work presents a patient-centered decision-making model to balance the trade-off between cost-based and drug-based contributions in epilepsy management. By linking medical decision-making through the equilibrium strategy, the study paves the way for personalized epilepsy treatment in JME management. Our model's application demonstrates that, under the equilibrium condition, the probability of selecting either VPA or LTG is 50%, indicating an equal preference for both drugs in managing JME. Sensitivity analyses on VPA and LTG parameters confirm the stability and reliability of this Nash equilibrium decision, reinforcing the model's applicability in clinical decision-making as well as assessing the stability and reliability of the Nash equilibrium decision in the treatment of JME. [ABSTRACT FROM AUTHOR]

AbstractWe examine a manufacturer’s strategic decision to its supplier’s potential technology infringement behavior within a co-opetitive supply chain, where the supplier serves as both the manufacturer’s production partner and market competitor. Our study investigates four potential reactions for the manufacturer when faced with the supplier’s possible infringement: no response, initiating patent litigation, entering a cross-licensing contract, or establishing a pure licensing agreement with the supplier. The supplier possesses the choice to decide whether to infringe on the manufacturer’s technology. By comparing equilibria among these models, we find that when the lawsuit winning rate is high, a lawsuit can demonstrate effectiveness, and a pure licensing contract can further fortify the positions of both parties. Surprisingly, a cross-licensing contract does not yield a similar effect and is absent from the equilibrium strategy in this scenario. Conversely, in cases where the lawsuit winning rate is low, litigation may not reach equilibrium. Instead, both parties could opt for either a pure licensing contract or a cross-licensing contract. Interestingly, while both types of licensing agreements significantly enhance outcomes for both parties in most instances, the no response model can still represent the equilibrium strategy under specific circumstances. [ABSTRACT FROM AUTHOR]

Internet finance is a new type of financial industry that is different from traditional finance.This study constructs an evolutionary game model between financial regulators and Internet financial institutions and discusses the strategy choices of the two participants under different circumstances. When analyzing the stable equilibrium strategy, the results show that when there are stable points in the game, Internet financial institutions tend to ‘excessive innovation’, while regulators’ strategies are affected by costs and benefits. When there is no stable point in the game, financial regulators and Internet financial institutions are in a continuous game of ‘moderate innovation – maintenance regulation – excessive innovation – strengthen regulation – moderate innovation.’ The study also provides policy recommendations to balance Internet financial innovation and regulation. [ABSTRACT FROM AUTHOR]

Keeping an intelligent agent under surveillance with an autonomous robot as it travels in the environment is one of the essential tasks in robotics. This work addresses a pursuit-evasion surveillance problem between two Differential Drive Robots moving on a plane without obstacles. One of them, the pursuer, is equipped with a limited field-of-view sensor and aims to maintain the other robot (evader) inside its detection region for as much time as possible. On the contrary, the evader wants to escape as soon as possible. Unlike prior studies that address the same problem, based on heuristic approaches, we frame it as a zero-sum differential game, and we use differential game theory to find a solution with theoretical guarantees. In particular, we compute the players' time-optimal motion strategies to achieve their goals near the end of the game and provide analytical expressions describing them. These strategies are in Nash equilibrium, meaning that any unilateral deviation by a player from these strategies does not provide such player benefit toward its goal. Our analysis exhibits the existence of a Transition Surface in which the evader switches its controls. We also determine the game's winner based on the players' initial configurations and velocities. [ABSTRACT FROM AUTHOR]

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability, (ii) if a strategy profile is played in two games, it is also played in every convex combination of these games, and (iii) players can shift probability arbitrarily between two indistinguishable actions, and deleting one of these actions has no effect. Our theorem implies that every equilibrium refinement violates at least one of these axioms. Moreover, every solution concept that approximately satisfies these axioms returns approximate Nash equilibria, even in natural subclasses of games, such as two‐player zero‐sum games, potential games, and graphical games. [ABSTRACT FROM AUTHOR]

This paper introduces mix‐zero‐sum differential (MZSD) game theory to address multi‐player tracking systems, offering a better understanding of the coexistence of cooperation and competition among players. Within this framework, we present an optimal safety tracking control (OSTC) method, which incorporates a control barrier function (CBF) into the value function to ensure that the tracking error remains within a specified range, thus guaranteeing safety while achieving optimization. Simultaneously, to eliminate the need for system dynamics, we propose a novel approach leveraging off‐policy integral reinforcement learning (IRL) technology to obtain the Nash equilibrium solution of the MZSD games. We establish a unique critics–actors neural network (NN) structure that updates concurrently. Furthermore, we analyze stability and convergence using the Lyapunov method. We conduct two simulations to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Forests are complex ecosystems that require integrated management to balance economic, social, and environmental dimensions. Conflicting objectives among stakeholders make optimal decision-making particularly challenging. This study seeks to balance the economic gains of forest harvesting with the goals of environmental conservation, with a focus on the Shafarood forest in Northern Iran. We applied multi-objective optimization and game theory to maximize the net present value (NPV) of forest harvesting while enhancing carbon sequestration. The research utilized data on stumpage prices, harvesting costs, tree density, volume per ha, growth rates, interest rates, carbon sequestration, and labour costs. Applying the epsilon-constraint method, we derived Pareto optimal solutions for a bi-objective model, and game theory was applied to negotiate between economic and environmental stakeholders. In the fifth round of bargaining, a Nash equilibrium was achieved between the two players. At this equilibrium point, the economic player achieved NPV from forest harvesting of 9001.884 (IRR 10,000/ha) and amount of carbon sequestration of 159.9383 tons/ha. Meanwhile, the environmental player achieved NPV from forest harvesting of 7861.248 (IRR 10,000/ha), along with a carbon sequestration of 159.9731 tons/ha. Results indicate significant trade-offs but reveal potential gains for both economic and environmental goals. These findings provide a robust framework for sustainable forest management and offer practical tools to support informed decision-making for diverse stakeholders. [ABSTRACT FROM AUTHOR]

The scarcity of land drives urban village redevelopment projects, which involve interest redistribution among stakeholders with distinct demands. This paper utilizes evolutionary game theory and simulation methods, constructing a tripartite game model under the institutional arrangement of bottom-up with private developer funding. This study identifies the stable strategies and evolutionary trends of the tripartite interactions under four distinct scenarios and validates these strategies through simulations. The redevelopment of XC village validates the assumptions of the model and theoretical analysis, suggesting that when private developers adopt forced demolition strategies, although villagers ultimately choose to sign the contract of property exchange, it can easily lead to social conflicts. These research findings can enlighten the government to form a tripartite alliance to smooth urban village redevelopment. [ABSTRACT FROM AUTHOR]

Game theory emerged as a science in the second half of the 20th century. It managed to prove itself well in the analysis of economic situations involving several subjects of economic activity (players), whose interests are completely or partially opposite. At the same time, in a number of cases, the solution of the game satisfied all players, but was not the most profitable (there was a Nash equilibrium), and in a number of other cases, it was possible to take into account the interests of all parties to the maximum (there was a Pareto optimal solution). The transfer of the principles of game theory to other areas turned out to have a number of difficulties associated, among other things, with the correct interpretation of strategies and gains of the parties in a conflict situation. For this reason, despite the obvious benefit from the possible application of game theory methods to problems of a fair distribution of quotas for catching fish and other seafood, this step has not been taken until recently. In this paper, we consider a scheme for applying the algorithms of the theory of bimatrix and cooperative games on the example of solving the problem of finding the percentage of the allowable catch of the Greenland halibut in the Barents Sea for two countries participating in the catch and give a meaningful interpretation of the results. The basis for the calculations was real data collected by the Russian–Norwegian Fisheries Commission in recent decades to determine the proportions of the catch of the indicated fish species in the respective sea zones. Since not all components of the payoff matrices of the players are uniquely determined, it became possible to perform a parametric analysis of the mathematical model of the conflict situation both in the search for an equilibrium solution and in the implementation of the arbitration scheme. The work is an extended and supplemented version of the report [2]. [ABSTRACT FROM AUTHOR]

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, with applications in diverse fields such as economics, political science, and biology. However, the Nash equilibrium may not always align with desired outcomes within the broader system. This article introduces a novel game engineering framework that tweaks strategic payoffs within a game to achieve a pre-defined desired Nash equilibrium while averting undesired ones. Leveraging mixed-integer linear programming, this framework identifies intricate combinations of players and strategies and optimal perturbations to their payoffs that enable the shift from undesirable Nash equilibria to more favorable ones. We demonstrate the effectiveness and scalability of our approach on games of varying complexity, ranging from simple prototype games such as the Prisoner's Dilemma and Snowdrift games with two or more players to complex game configurations with up to 10 6 entries in the payoff matrix. These studies showcase the capability of this framework in efficiently identifying the alternative ways of reshaping strategic payoffs to secure desired Nash equilibria and preclude undesired equilibrium states. Our game engineering framework offers a versatile toolkit for precision strategic decision-making with far-reaching implications across diverse domains. [ABSTRACT FROM AUTHOR]

Coordinating with others is part of our everyday experience. Previous studies using sensorimotor coordination games suggest that human dyads develop coordination strategies that can be interpreted as Nash equilibria. However, if the players are uncertain about what their partner is doing, they develop coordination strategies which are robust to the actual partner's actions. This has suggested that humans select their actions based on an explicit prediction of what the partner will be doing—a partner model—which is probabilistic by nature. However, the mechanisms underlying the development of a joint coordination over repeated trials remain unknown. Very much like sensorimotor adaptation of individuals to external perturbations (eg force fields or visual rotations), dynamical models may help to understand how joint coordination develops over repeated trials. Here we present a general computational model—based on game theory and Bayesian estimation—designed to understand the mechanisms underlying the development of a joint coordination over repeated trials. Joint tasks are modeled as quadratic games, where each participant's task is expressed as a quadratic cost function. Each participant predicts their partner's next move (partner model) by optimally combining predictions and sensory observations, and selects their actions through a stochastic optimization of its expected cost, given the partner model. The model parameters include perceptual uncertainty (sensory noise), partner representation (retention rate and internale noise), uncertainty in action selection and its rate of decay (which can be interpreted as the action's learning rate). The model can be used in two ways: (i) to simulate interactive behaviors, thus helping to make specific predictions in the context of a given joint action scenario; and (ii) to analyze the action time series in actual experiments, thus providing quantitative metrics that describe individual behaviors during an actual joint action. We demonstrate the model in a variety of joint action scenarios. In a sensorimotor version of the Stag Hunt game, the model predicts that different representations of the partner lead to different Nash equilibria. In a joint two via-point (2-VP) reaching task, in which the actions consist of complex trajectories, the model captures well the observed temporal evolution of performance. For this task we also estimated the model parameters from experimental observations, which provided a comprehensive characterization of individual dyad participants. Computational models of joint action may help identifying the factors preventing or facilitating the development of coordination. They can be used in clinical settings, to interpret the observed behaviors in individuals with impaired interaction capabilities. They may also provide a theoretical basis to devise artificial agents that establish forms of coordination that facilitate neuromotor recovery. Author summary: Acting together (joint action) is part of everyday experience. But, how do we learn to coordinate with others and collaborate? Using a combination of experiments and computational models we show that through multiple repetitions of the same joint task we select the action which represents the 'best response' to what we believe our opponent will do. Such a belief about our partner (partner model) is developed gradually, by optimally combining prior assumptions (how repeatable or how erratic our opponent behaves) with sensory information about our opponent's past actions. Rooted in game theory and Bayesian estimation, the model accounts for the development of the mutual 'trust' among partners which is essential for establishing a mutually advantageous collaboration, and explains how we combine decisions and movements in complex coordination scenarios. The model can be used as a generative tool, to simulate the development of coordination in a specific joint action scenario, and as an analytic tool to characterize the individual traits or defects in the ability to establish collaborations. [ABSTRACT FROM AUTHOR]

Deep neural networks (DNNs) are fundamental to modern applications like face recognition and autonomous driving. However, their security is a significant concern due to various integrity risks, such as backdoor attacks. In these attacks, compromised training data introduce malicious behaviors into the DNN, which can be exploited during inference or deployment. This paper presents a novel game-theoretic approach to model the interactions between an attacker and a defender in the context of a DNN backdoor attack. The contribution of this approach is multifaceted. First, it models the interaction between the attacker and the defender using a game-theoretic framework. Second, it designs a utility function that captures the objectives of both parties, integrating clean data accuracy and attack success rate. Third, it reduces the game model to a two-player zero-sum game, allowing for the identification of Nash equilibrium points through linear programming and a thorough analysis of equilibrium strategies. Additionally, the framework provides varying levels of flexibility regarding the control afforded to each player, thereby representing a range of real-world scenarios. Through extensive numerical simulations, the paper demonstrates the validity of the proposed framework and identifies insightful equilibrium points that guide both players in following their optimal strategies under different assumptions. The results indicate that fully using attack or defense capabilities is not always the optimal strategy for either party. Instead, attackers must balance inducing errors and minimizing the information conveyed to the defender, while defenders should focus on minimizing attack risks while preserving benign sample performance. These findings underscore the effectiveness and versatility of the proposed approach, showcasing optimal strategies across different game scenarios and highlighting its potential to enhance DNN security against backdoor attacks. [ABSTRACT FROM AUTHOR]

Weapon target assignment is a critical challenge in military contexts. Traditionally, commanding officers manually decide weapon assignments, but the problem's complexity has grown over time. To address this, automated systems have been introduced. These systems fall into two categories, which are static (time-independent) and dynamic (considering changes over time). Static systems solve the problem for a single time step without considering temporal changes. Dynamic systems incorporate time as a variable, adapting to evolving scenarios. Two main approaches exist, which are asset-based and target-based. Asset-based approach maximizes the survival probability of assets, which is our focus in this study. We propose a solution using game theory that spans the entire area and all time frames. We employ game theory, treating continuous functions of time as utility functions for vessels. Continuous probability-to-kill values for weapons are defined across the area. Threat trajectories yield continuous kill probabilities for the weapons, translating to vessel utility. To avoid inefficiencies, we align individual vessel utility with global utility. The Nash Equilibrium provides the optimal weapon assignment strategy. Our study uses a naval environment for analysis. In summary, our research leverages game theory to dynamically assign weapons to naval vessels, aiming to maximize asset survival. [ABSTRACT FROM AUTHOR]

In game theory, mechanism design is concerned with the design of incentives so that a desirable outcome will be achieved under the assumption that players act rationally. In this paper, we explore the concept of equilibrium design, where incentives are designed to obtain a desirable equilibrium that satisfies a specific temporal logic property. Our study is based on a framework where system specifications are represented as temporal logic formulae, games as quantitative concurrent game structures, and players' goals as meanpayoff objectives. We consider system specifications given by LTL and GR(1) formulae, and show that designing incentives to ensure that a given temporal logic property is satisfied on some/every Nash equilibrium of the game can be achieved in PSPACE for LTL properties and in NP/SP2 for GR(1) specifications. We also examine the complexity of related decision and optimisation problems, such as optimality and uniqueness of solutions, as well as considering social welfare, and show that the complexities of these problems lie within the polynomial hierarchy. Equilibrium design can be used as an alternative solution to rational synthesis and verification problems for concurrent games with mean-payoff objectives when no solution exists or as a technique to repair concurrent games with undesirable Nash equilibria in an optimal way. [ABSTRACT FROM AUTHOR]

In this article, a game theoretic non‐cooperative dynamic target tracking algorithm that empowers defensive unmanned aerial vehicles (UAVs), with directional sensing capabilities to track and collect information on intrusive UAVs, is proposed. Specifically, defenders aim to maximize the collection of identity information from intruders possessing anti‐tracking and evading capabilities, while simultaneously preventing their entry into protected areas. Game theory is employed to determine the optimal confrontation paths for defenders against the intruders. The probability perception model is utilized for evaluating the dynamic target tracking capability and designing a tracking merit function to assess tracking performance, taking into account both the target's position and the perception relative angle. Furthermore, considering the dynamic interactive behaviors between intruders and defenders, the iterative linear quadratic game (ILQG) algorithm is employed to solve the Nash equilibrium of the non‐cooperative target tracking game. Through simulation experiments, the effectiveness of the proposed algorithm in accomplishing multi‐agent dynamic target tracking tasks is demonstrated and the performance of the algorithm under varying parameters in the intruder's cost function is evaluated, which represent different intrusion intentions. [ABSTRACT FROM AUTHOR]

This paper models games where the strategies are nodes of a graph G (we denote them as G-games) and in presence of coalition structures. The cases of one-shot and repeated games are presented. In the latter situation, coalitions are assumed to move from a strategy to another one under the constraint that they are adjacent in the graph. We introduce novel concepts of pure and mixed equilibria which are comparable with classical Nash and Berge equilibria. A Folk Theorem for G-games of repeated type is presented. [ABSTRACT FROM AUTHOR]

Traditional jamming technologies have become less effective with the development of anti-jamming technologies, especially with the appearance of intelligent transmitters, which can adaptively adjust their transmission strategies. To deal with intelligent transmitters, in this paper, a game-based intelligent jamming scheme is proposed. Considering that the intelligent transmitter has multiple transmission strategy sets whose prior probabilities are unknown to the jammer, we first model the interaction between the transmitter and the jammer as a dynamic game with incomplete information. Then the perfect Bayesian equilibrium is derived based on assumptions of some prior information. For more practical applications when no prior information about the transmitter is available at the jammer, a Q-learning-based method is proposed to find an intelligent jamming strategy by exploiting the sensing results of the wireless communications. The design of the jammer's reward function is guided by the game utility and the reward is calculated based on the Acknowledgement/Negative Acknowledgement feedback of the receiver. Simulation results show that the proposed scheme has only 0.5 % loss in jamming utility compared to that of the perfect Bayesian equilibrium strategy. Compared to existing jamming schemes, a higher packet error rate can be achieved by the proposed scheme by consuming less jamming power. [ABSTRACT FROM AUTHOR]

This article introduces a class of Nash games among Stackelberg players (NASPs), namely, a class of simultaneous noncooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a Stackelberg game where a leader optimizes a (parametrized) linear objective function subject to linear constraints, whereas its followers solve convex quadratic problems subject to the standard optimistic assumption. Although we prove that deciding if a NASP instance admits a Nash equilibrium is generally a Σ2p -hard decision problem, we devise two exact and computationally efficient algorithms to compute and select Nash equilibria or certify that no equilibrium exists. We use NASPs to model the hierarchical interactions of international energy markets where climate change aware regulators oversee the operations of profit-driven energy producers. By combining real-world data with our models, we find that Nash equilibria provide informative, and often counterintuitive, managerial insights for market regulators. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.03418. [ABSTRACT FROM AUTHOR]

With the rapid advancement of Internet of Vehicles (IoV) technology, the demands for real-time navigation, advanced driver-assistance systems (ADAS), vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications, and multimedia entertainment systems have made in-vehicle applications increasingly computing-intensive and delay-sensitive. These applications require significant computing resources, which can overwhelm the limited computing capabilities of vehicle terminals despite advancements in computing hardware due to the complexity of tasks, energy consumption, and cost constraints. To address this issue in IoV-based edge computing, particularly in scenarios where available computing resources in vehicles are scarce, a multi-master and multi-slave double-layer game model is proposed, which is based on task offloading and pricing strategies. The establishment of Nash equilibrium of the game is proven, and a distributed artificial bee colonies algorithm is employed to achieve game equilibrium. Our proposed solution addresses these bottlenecks by leveraging a game-theoretic approach for task offloading and resource allocation in mobile edge computing (MEC)-enabled IoV environments. Simulation results demonstrate that the proposed scheme outperforms existing solutions in terms of convergence speed and system utility. Specifically, the total revenue achieved by our scheme surpasses other algorithms by at least 8.98%. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) has permeated various fields relevant to our lives. In these applications, countless IoT devices transmit vast amounts of data, which often carry important and private information. To prevent malicious users from spoofing these information, the first critical step is effective authentication. Physical Layer Authentication (PLA) employs unique characteristics inherent to wireless signals and physical devices and is promising in the IoT due to its flexibility, low complexity, and transparency to higher layer protocols. In this paper, the focus is on the interaction between multiple malicious spoofers and legitimate receivers in the PLA process. First, the interaction is formulated as a static spoof detection game by including the spoofers and receivers as players. The best authentication threshold of the receiver and the attack rate of the spoofers are consideblack as Nash Equilibrium (NE). Then, closed-form expressions are derived for all NEs in the static environment in three cases: multiplayer games, zero-sum games with collisions, and zero-sum games without collisions. Considering the dynamic environment, a Multi-Agent Deep Deterministic Policy Gradient (MADDPG) algorithm is proposed to analyze the interactions of receiver and spoofers. Last, comprehensive simulation experiments are conducted and demonstrate the impact of environmental parameters on the NEs, which provides guidance to design effective PLA schemes.

Congestion games offer a primary model in the study of pure Nash equilibria in non-cooperative games, and a number of generalized models have been proposed in the literature. One line of generalization includes weighted congestion games, in which the cost of a resource is a function of the total weight of the players choosing that resource. Another line includes congestion games with mixed costs, in which the cost imposed on a player is a convex combination of the total cost and the maximum cost of the resources in her strategy. This model is further generalized to that of congestion games with non-additive aggregation. For the above models, the existence of a pure Nash equilibrium is proved under some assumptions, including the case in which the strategy space of each player is the base family of a matroid and the case in which the cost functions have a certain kind of monotonicity. In this paper, we deal with common generalizations of these two lines, namely weighted matroid congestion games with non-additive aggregation, and its further generalization. Our main technical contribution is a proof of the existence of pure Nash equilibria in these generalized models under a simplified assumption on the monotonicity, which provides a common extension of the previous results. We also present an extension on the existence of pure Nash equilibria in weighted matroid congestion games with mixed costs. [ABSTRACT FROM AUTHOR]

In recent years, problems of nonzero-sum investment and reinsurance games have received a lot of attention from scholars. However, for practical consideration, there is also consumption in the operation process of insurers, which is rarely taken into account by scholars. This paper integrated the consumption problem into nonzero-sum investment-reinsurance problems, and studied the nonzero-sum investment, consumption, and reinsurance game between two competitive insurers. Each insurer was allowed to purchase proportional reinsurance and invest in a financial market consisting of a risk-free asset and a risky asset, and the price process of the risky asset was described by the constant elasticity of variance (CEV) model. Moreover, the consumption behavior of each insurer was also considered. The main objective of each insurer was to maximize the utility of his terminal surplus and accumulated consumption relative to that of his competitor. Based on the stochastic differential game theory, we obtained the Hamilton-Jacobi-Bellman (HJB) equations for both insurers and derived the equilibrium strategies and the equilibrium value function. Numerical examples were given in the end to illustrate the influence of model parameters on the equilibrium strategies. [ABSTRACT FROM AUTHOR]

To study the rescue behavior of respondents to major sudden traffic accidents, this study considered an accident rescue system composed of responses from the government and social organizations. Based on differential game theory, three game models of independent rescue, cooperative rescue, and government-subsidized rescue were constructed to assess the responses from the government and social organizations. The equilibrium strategy and an optimal rescue trajectory for the government and social organizations were obtained. To improve the effectiveness of the rescue efforts of the government and social organizations, the maximum entropy optimization model was applied to quantify the risk of road congestion and potential secondary disaster risks, and the impact of key parameters such as road congestion risk and rescue timeliness on the effectiveness of the rescue efforts and its socioeconomic benefits were analyzed. When certain conditions were met, the level of effective assistance and total socioeconomic benefits displayed an increasing trend from independent assistance by the government and social organizations to government-subsidized assistance, and then to cooperative assistance by both parties. The decay rate of assistance effectiveness had an inverse impact on the effective rescue response. Additionally, using the maximum entropy model to quantify the degree of congestion risk not only enabled the influencing factors at the accident site to be considered, but also helped to improve the socioeconomic benefits obtained by governments and social organizations in their rescue response to major traffic accidents. Finally, through a sensitivity analysis of the key parameters, i.e., the direct economic losses recovered by the government and social organizations during their rescue efforts, the value generated by the potential economic activities of the government and social organizations, the impact coefficient of the government and social organization's rescue efforts on potential economic activities, and the impact coefficient of government and social organization investment in rescue, it was found that they all positively affected the effectiveness of the rescue. [ABSTRACT FROM AUTHOR]

With the rapid development of technologies and applications, extending from trusted environments to untrusted environments is the development trend of Internet of Things (IoT) applications. Due to the limited resources of nodes and the rise of edge computing, more and more IoT applications are required to have task delegation functions. Delegating IoT tasks in untrusted environments has to solve two problems: First, how to evaluate the trustworthiness of nodes so that requesters can delegate tasks to trusted providers; the second is how to ensure the successful implementation of the task delegation between the requester and the provider. While trust models are often used to solve the first problem, the lack of ability to describe transactions between the requester and the provider makes them unsuitable for solving the second problem. In recent years, game theory has been more applied to task delegation. By setting appropriate utility functions, game theory can ensure the successful implementation of task delegation. However, since it is unable to evaluate the trustworthiness of nodes, game theory cannot solve the first problem. This paper combines the advantages of trust models and game theory to construct a game of three-party task delegation based on trust to explore a solution to problems of IoT task delegation in an untrusted environment. Finally, aiming at the problem that setting essential parameter values of trust models is empirical and experimental, this paper theoretically discusses how to set these values in an untrusted environment. [ABSTRACT FROM AUTHOR]

Summary: Due to geographical factors, it is impossible to build large‐scale communication network infrastructure in remote areas, which leads to poor network communication quality in these areas and a series of delay‐sensitive tasks cannot be timely processed and responded. Aiming at the problem of limited coverage in remote areas, the space‐air‐ground integrated networks (SAGIN) combined with mobile edge computing (MEC) can provide low latency and high reliability transmission for offloading delay‐sensitive tasks for users in remote areas. Considering the strong limitation of satellite resources in the space‐ground integrated network and insufficient energy of local user equipment, firstly, a satellite‐UAV cluster‐ground three‐layer edge computing network architecture is proposed in this paper. Under the condition that the delay requirements of various ground tasks are met, the task offloading problem is transformed into a Stackelberg game between ground user equipment and edge servers. In addition, it is proved that the existence of Nash equilibrium in non‐cooperative game between ground user equipment by using potential game. Finally, a Nash equilibrium iterative offloading algorithm based on Stackelberg game (NEIO‐SG) is proposed to find the optimal offloading strategy for tasks to minimize the system offloading cost and the optimal forwarding percentage strategy for offloading tasks to maximize the utility function of the edge server. Simulation results show that compared to other baseline algorithms, NEIO‐SG reduces the total system latency during task offloading by about 13%$$ \% $$ and the energy consumption of the edge server by about 35%$$ \% $$. [ABSTRACT FROM AUTHOR]

Thanks to reinforcement learning (RL), decision‐making is more convenient and more economical in different situations with high uncertainty. In line with the same fact, it is proposed that prosumers can apply RL to earn more profit in the transactive energy market (TEM). In this article, an environment that represents a novel framework of TEM is designed, where all participants send their bids to this framework and receive their profit from it. Also, new state‐action spaces are designed for sellers and buyers so that they can apply the Soft Actor‐Critic (SAC) algorithm to converge to the best policy. A brief of this algorithm, which is for continuous state‐action space, is described. First, this algorithm is implemented for a single agent (a seller and a buyer). Then we consider all players including sellers and buyers who can apply this algorithm as Multi‐Agent. In this situation, there is a comprehensive game between participants that is investigated, and it is analyzed whether the players converge to the Nash equilibrium (NE) in this game. Finally, numerical results for the IEEE 33‐bus distribution power system illustrate the effectiveness of the new framework for TEM, increasing sellers' and buyers' profits by applying SAC with the new state‐action spaces. SAC is implemented as a Multi‐Agent, demonstrating that players converge to a singular or one of the multiple NEs in this game. The results demonstrate that buyers converge to their optimal policies within 80 days, while sellers achieve optimality after 150 days in the games created between all participants. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of tariff escalation on multinational suppliers relocating their production capacity to tariff-preferential regions with unreliable supply caused by low-production technology. We build a game theory model to analyze this issue based on three decisions for supplier-capacity relocation: no relocation, partial relocation, and full relocation. Our analysis finds that when tariffs are low or the production technology of the base in a preferential tariff region is not advanced, the supplier tends to adopt a partial-relocation strategy, but this strategy may be hindered by a manufacturer's order-allocation decision, leading to a no-relocation strategy as the supply chain's equilibrium. This may result in greater losses for the supplier. When tariffs are high or the production technology of the base in the preferential tariff region is advanced, the equilibrium strategy for the supply chain shifts to a full-relocation strategy. Interestingly, in the partial-relocation strategy, the higher production technology in the preferential tariff region negatively impacts the manufacturer's expected profits but benefits the supplier's expected profits due to the increased double marginalization. Finally, we find that the supplier can reduce the impact of tariffs by relocating their production capacity, especially with the partial-relocation strategy, as the supplier is always motivated to improve the production technology of the base in the preferential tariff region, with a potential purpose of transferring tariff costs to the manufacturer and consumers. [ABSTRACT FROM AUTHOR]

The rapid rise of live-streaming selling and the increasing diversity of e-commerce channels have sparked ongoing debates regarding product pricing power. This price competition behaviour of online dual channels triggered by the supply-side pricing dilemma is a topic of significant research interest and forms the focal point of this paper. Therefore, we leverage the principles of game theory to construct a three-party evolutionary game model consisting of a brand, a steamer, and a traditional e-commerce platform. Within this framework, the brand holds the primary pricing authority. Our analysis examines the equilibrium strategies adopted by the various players under diverse scenarios and explores how the evolving behaviours of these parties impact the overall game system. Additionally, we employ the "people-goods-scene" perspective to deconstruct the intricate dynamics within this complex supply chain ecosystem. Our findings reveal two distinct evolutionary stable strategies: one in which brands maintain a stance against low-price negotiation, streamers avoid bargaining, and platforms avoid providing subsidies; the other in which brands are open to negotiating low prices, streamers engage in bargaining, and platforms provide subsidies. Notably, in most cases, brands tend to avoid explicitly stating their opposition to low-price negotiation. However, if a brand's strategy shifts towards rejecting such negotiation, the negative implications of price wars across channels become a critical consideration. Conversely, when a brand opts for a more concessive pricing strategy, we need to consider the potential positive impacts of low-price competition. [ABSTRACT FROM AUTHOR]

For intelligent systems, argumentation is a very important factor to point out in Artificial Intelligence (AI) as it represents an essential component. It is one of the critical approaches to making a decision, whereas Dung introduces a mathematical model that classifies attacks among arguments based on ordered pairs. Furthermore, weights’ addition to the arguments is one of the most important developments. It is done by several methods of weight calculation; hence, the Fuzzy weights method is a suitable method when working with game theory (GT). To this end, this paper introduced the GT in a Nash equilibrium method to redraw the acceptable arguments. It depends on the fuzzy weight for reducing the acceptable arguments and acceptable attacks between those arguments. This paper provides an automatic model for reducing the number of arguments and attacks between them called the shorthand model based on the gaming argumentation framework SGAF by extending the gaming argumentation framework GAF. This work uses the Cash on Delivery (COD) Payment Model as a case study. [ABSTRACT FROM AUTHOR]

Nash equilibrium is arguably the most fundamental concept in game theory, which is used to analyze and predict the behavior of the players. In many games, there exist multiple equilibria, with different expected payoffs for the players, which in turn raises the question of equilibrium selection. In this paper, we study the NP -hard problem of identifying a socially optimal Nash equilibrium in two-player normal-form games (called bimatrix games), which may be represented by a mixed integer linear program (MILP). We characterize the properties of the equilibria and develop several classes of valid inequalities accordingly. We use these theoretical results to provide a decomposition-based reformulation of the MILP, which we solve by a branch-and-cut algorithm. Our extensive computational experiments demonstrate superiority of our approach over solving the MILP formulation through feeding it into a commercial solver or through the "traditional" Benders' decomposition. Of note, our proposed approach can find provably optimal solutions for many instances. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms. Funding: This work was supported by the National Institute of Dental and Craniofacial Research [Grant R01DE028283]. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The funding agreements ensured the authors' independence in designing the study, interpreting the data, writing, and publishing the report. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0072) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0072). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Severe Acute Respiratory Syndrome (SARS) is a highly contagious viral disease with high mortality rate. There is no vaccine against SARS, but the spread can be limited by masking or social distancing. In this paper we implement a game-theoretic model of voluntary precautions against SARS. We build on the compartmental ODE model of the 2003 SARS epidemic. We assume that susceptible individuals can mask and/or limit contacts with others in order to decrease their chances of contracting SARS. Since the risk of SARS infection depends on the actions of others, this creates a public goods game. We find the Nash equilibrium, the solution of the game, which is the optimal voluntary level of precautions the individuals should take. We also study the effects of such actions on the spread of SARS and show that the effect significantly depends on the individual cost of the precautions. As soon as the cost rises above a critical threshold, the individuals will have no incentive to use any kind of voluntary precaution. [ABSTRACT FROM AUTHOR]

We consider first-price auctions with independent and private valuations that have asymmetric valuation distributions and supports. We first show the existence of equilibrium in these auctions through a perturbation approach, thereby establishing that the limit of Bayesian Nash equilibria (BNE) of such perturbed auctions is indeed the Bayesian Nash equilibrium (BNE) of the limit auction with asymmetric supports. We then characterize this BNE and show that the ε -equilibrium (ε -BNE) of the auction with asymmetric supports is a BNE of "close" auctions with common supports. We then demonstrate some numerical examples. [ABSTRACT FROM AUTHOR]

Purpose: During the last decades, the strategic interaction between the monetary authority, i.e. the central bank, and the financial authority, i.e. the central government, has attracted the attention of many economic policymakers, in both developing and advanced countries. A method that plays an important role in the analysis of the strategic confrontation between these two institutions is analysis based on the game theory. This theory has wide applications in various branches of science, including economics, engineering, biology, political science, and military science. The behaviour of each person or player is not only affected by the individual’s own decisions, but also it depends on the behaviour and decisions of other players. The government aims to foster robust economic growth through budgetary expenses, while the central bank aims to maintain the stability of inflation through interest rate mechanisms. Studies show that the different goals of the central bank and the government are a challenge for the economic stability of a country. The optimal solution for officials is to coordinate their actions and decisions, because coordination improves the situation of the decision makers in both arenas. In Iran's economy, the issue of coordination or lack of it in the implementation of macroeconomic policies is of particular importance for monetary and financial authorities. Therefore, in this study, the interaction between these two groups of authorities is investigated through the game theory in normal forms. Methodology: Regarding policy coordination between the government and the central bank, there are two types of strategic interaction, which are very useful and important in the analysis of equilibrium solutions. One includes non-cooperative games between two officials, and the other includes cooperative games. The games in which joint action contracts are applicable are called cooperative games, but the games in which such joint actions are not possible and individual participants must be allowed to act in their own interests are called non-cooperative games. To establish equilibrium in this game, three concepts are used, including Nash equilibrium, Berge equilibrium and Greedy Scaler equilibrium. In a Nash case, each player individually and self-interestedly seeks to maximize his profit. Conversely, in Berge equilibrium, players exhibit altruistic behaviours versus their opponents. In Greedy equilibrium, however, players engage in a semi-cooperative game, striving to advance their shared interests through the formation of coalitions. Also, the Prisoner’s Dilemma has been investigated for the strategic confrontation of the two groups of policy makers. This game is a classic cooperation and choice problem based on the assumption of selfish human motives. Blinder (1983) designed a policy decision-making problem in the framework of the Prisoner’s Dilemma. Findings and discussion: The outcomes of this game reveal that, in a two-strategy situation, the Nash equilibrium occurs when both the government and the central bank adopt contractionary policy strategies. In this game, the economy does not enter into the prisoner's dilemma, but it is the Pareto optimal. Conversely, in the Berge equilibrium, the scenario arises where the government pursues an expansionary fiscal strategy while the central bank implements a contractionary monetary strategy. In addition, many situations of Greedy equilibrium include both Nash and Berge equilibria. The results for Iran's economy show that the implementation of a balanced and optimization Nash policy by the government and the central bank (contraction fiscal and monetary policy) brings the most benefits for the government. The implementation of an optimal Berge policy by the government and the central bank involves the most benefits for the central bank. However, the results show that, in the first scenario, based on the reviewed information, there are two Greedy equilibria, Nash equilibrium and Berge equilibrium. The first Greedy equilibrium corresponds to the Nash equilibrium, and the second one corresponds to the Berge equilibrium. Therefore, if the government and the central bank follow a semi-cooperative game, both Nash and Berge equilibria can be reached. The equilibrium extracted from the second scenario is more beneficial than the one from the first scenario. Also, in the semi-cooperative game, a more favourable balance can still be achieved. So, the government and the central bank seek the highest profit by forming a coalition and cooperating with each other. During the first development plan, the Nash equilibrium brings the most economic growth for the government, and, during the third and fourth development plans, the central bank faces the lowest inflation in the Nash equilibrium. However, in the Berge balance, the government experiences the highest economic growth in the third development plan. In this situation, the central bank sees the lowest level of inflation in both the third and fourth development plans. In addition, in the optimal Nash equilibrium, compared to the other equilibria, the government achieves the maximum result, and, in the optimal policy of the central bank, it will achieve the lowest inflation. Conclusions and policy implications: It is suggested to the policymakers to pay attention to the type of game designed in adopting their policies. So, if these authorities seek to achieve a non-cooperative game, they should follow the strategy of contractionary monetary and financial policies. Also, to reach an altruistic equilibrium and mutual support, the central bank should follow a contractionary monetary policy, and the government should follow an expansionary fiscal policy. For future studies, it is suggested that the role of a third actor, such as speculators or parliament (legislature), be seen in the game between the government and the central bank. [ABSTRACT FROM AUTHOR]

The purpose of this research is to develop the outsourcing model of the bank’s electronic banking services using game theory to identify the equilibrium and win-win strategies between the bank and the applicant companies. For this purpose, an interview was held with bank and company experts. After qualitative data analysis,16 strategies were identified for the parties. According to the compatibility of the identified strategies with the marketing mix, the results were grouped into 4 product groups, price, distribution and promotion. Since the identified strategies did not have the same value for the parties, to identify the weight of the strategies. A pairwise comparison questionnaire was used and the opinions of experts from each side were collected separately. The analytical Hierarchy process was used to obtain the weight of each index and the Inconsistency Ratio index was used to check the reliability of the obtained results. After identifying the weight of the strategies, the game environment was implemented and according to the 16 identified strategies, 65536 scenarios were implemented for each side. After performing calculations, 8 scenarios with the same outcomes were identified as equilibrium scenarios or Nash Equilibrium games. The scenario that had the most consequences for the parties was introduced as the result of the game. [ABSTRACT FROM AUTHOR]