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Games

Games is a scholarly, peer-reviewed, open access journal of studies on game theory and its applications published bimonthly online by MDPI.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, ESCI (Web of Science), MathSciNet, zbMATH, RePEc, EconLit, EconBiz, and other databases.
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 22.6 days after submission; acceptance to publication is undertaken in 3.9 days (median values for papers published in this journal in the first half of 2024).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.

Impact Factor: 0.6 (2023)

Imprint Information Journal Flyer Open Access ISSN: 2073-4336

Latest Articles

22 pages, 722 KiB

Open AccessArticle

Nash Equilibria and Undecidability in Generic Physical Interactions—A Free Energy Perspective

by Chris Fields and James F. Glazebrook

Games 2024, 15(5), 30; https://doi.org/10.3390/g15050030 - 26 Aug 2024

We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in [...] Read more.

We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in a new light in so far as the incompleteness and undecidability of the concept, as well as the nature of strategies in general, can be seen as the consequences of certain no-go theorems. We show that games of the generic imitation type follow a circularity of idealization that includes the good regulator theorem, generalized synchrony, and undecidability of the Turing test. We discuss Bayesian games in the light of Bell non-locality and establish the basics of quantum games, which we relate to local operations and classical communication protocols. In this light, we also review the rationality of gaming strategies from the players’ point of view. Full article

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10 pages, 2074 KiB

Open AccessArticle

Cournot Duopoly with Cost Asymmetry and Balanced Budget Specific Taxes and Subsidies

by Olivia Kay

Games 2024, 15(4), 29; https://doi.org/10.3390/g15040029 - 19 Aug 2024

This paper extends the Cournot duopoly model by allowing the government to impose firm-dependent specific taxes or subsidies while keeping the budget balanced. It considers two possible government goals: maximizing the social surplus and maximizing the consumer surplus. It shows that, with identical [...] Read more.

This paper extends the Cournot duopoly model by allowing the government to impose firm-dependent specific taxes or subsidies while keeping the budget balanced. It considers two possible government goals: maximizing the social surplus and maximizing the consumer surplus. It shows that, with identical firms, the best government policy is not to intervene. In the case of cost asymmetry, social surplus and consumer surplus maximization goals require opposite strategies: to maximize the social surplus, the government should tax the high-cost firm driving the economy toward monopoly and increasing productive efficiency at the expense of lower production. In the case of consumer surplus maximization, the tax should be imposed on the low-cost firm reducing the gap between the firms’ outputs. Such a strategy, however, increases productive inefficiency and reduces the social surplus. Full article

(This article belongs to the Section Applied Game Theory)

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27 pages, 363 KiB

Open AccessReview

A Review of Attacker–Defender Games and Cyber Security

by Kjell Hausken, Jonathan W. Welburn and Jun Zhuang

Games 2024, 15(4), 28; https://doi.org/10.3390/g15040028 - 14 Aug 2024

The focus of this review is the long and broad history of attacker–defender games as a foundation for the narrower and shorter history of cyber security. The purpose is to illustrate the role of game theory in cyber security and which areas have [...] Read more.

The focus of this review is the long and broad history of attacker–defender games as a foundation for the narrower and shorter history of cyber security. The purpose is to illustrate the role of game theory in cyber security and which areas have received attention and to indicate future research directions. The methodology uses the search terms game theory, attack, defense, and cyber security in Web of Science, augmented with the authors’ knowledge of the field. Games may involve multiple attackers and defenders over multiple periods. Defense involves security screening and inspection, the detection of invaders, jamming, secrecy, and deception. Incomplete information is reviewed due to its inevitable presence in cyber security. The findings pertain to players sharing information weighted against the security investment, influenced by social planning. Attackers stockpile zero-day cyber vulnerabilities. Defenders build deterrent resilient systems. Stochastic cyber security games play a role due to uncertainty and the need to build probabilistic models. Such games can be further developed. Cyber security games based on traffic and transportation are reviewed; they are influenced by the more extensive communication of GPS data. Such games should be extended to comprise air, land, and sea. Finally, cyber security education and board games are reviewed, which play a prominent role. Full article

(This article belongs to the Special Issue Game Theory and Risk Analysis)

26 pages, 404 KiB

Open AccessArticle

On Hurwicz Preferences in Psychological Games

by Giuseppe De Marco, Maria Romaniello and Alba Roviello

Games 2024, 15(4), 27; https://doi.org/10.3390/g15040027 - 30 Jul 2024

The literature on strategic ambiguity in classical games provides generalized notions of equilibrium in which each player best responds to ambiguous or imprecise beliefs about his opponents’ strategic choices. In a recent paper, strategic ambiguity has been extended to psychological games, by [...] Read more.

The literature on strategic ambiguity in classical games provides generalized notions of equilibrium in which each player best responds to ambiguous or imprecise beliefs about his opponents’ strategic choices. In a recent paper, strategic ambiguity has been extended to psychological games, by taking into account ambiguous hierarchies of beliefs and max–min preferences. Given that this kind of preference seems too restrictive as a general method to evaluate decisions, in this paper we extend the analysis by taking into account

α

-max–min preferences in which decisions are evaluated by a convex combination of the worst-case (with weight

α

) and the best-case (with weight

1 - α

) scenarios. We define the

α

-max–min psychological Nash equilibrium; an illustrative example shows that the set of equilibria is affected by the parameter

α

and the larger the ambiguity, the greater the effect. We also provide a result of stability of the equilibria with respect to perturbations that involve the attitudes toward ambiguity, the structure of ambiguity, and the payoff functions: converging sequences of equilibria of perturbed games converge to equilibria of the unperturbed game as the perturbation vanishes. Surprisingly, a final example shows that the existence of equilibria is not guaranteed for every value of

α

. Full article

11 pages, 245 KiB

Open AccessArticle

Auctioning off a Non-Rivalrous Good with Interference

by Alison Watts

Games 2024, 15(4), 26; https://doi.org/10.3390/g15040026 - 11 Jul 2024

Auctions are a prevalent way to exchange goods and are well-studied for the exchange of rivalrous goods, but are less studied for non-rivalrous goods. I examine an auction framework where the good sold can be used simultaneously by multiple bidders if their use [...] Read more.

Auctions are a prevalent way to exchange goods and are well-studied for the exchange of rivalrous goods, but are less studied for non-rivalrous goods. I examine an auction framework where the good sold can be used simultaneously by multiple bidders if their use does not conflict with others; this simultaneous use directly affects the efficiency of the auction. A timely example includes the auctioning off of a radio spectrum by a licensed primary user to unlicensed secondary users who can use the spectrum simultaneously if they are located far enough apart to not cause interference. I examine a uniform price auction over non-conflicting groups and examine how non-rivalry impacts both efficiency and collusion. Conditions are given under which an auction over groups generates higher social welfare than an individual auction. Additional conditions are given under which collusion in a group auction results in higher prices. Full article

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23 pages, 2937 KiB

Open AccessArticle

One Justice for All? Social Dilemmas, Environmental Risks and Different Notions of Distributive Justice

by Ulf Liebe, Heidi Bruderer Enzler, Andreas Diekmann and Peter Preisendörfer

Games 2024, 15(4), 25; https://doi.org/10.3390/g15040025 - 1 Jul 2024

A just or fair distribution of environmental bads and goods is important for solving environmental social dilemmas and is a core idea of environmental justice politics and research. Environmental justice is mostly associated with egalitarianism as the sole justice principle for all people. [...] Read more.

A just or fair distribution of environmental bads and goods is important for solving environmental social dilemmas and is a core idea of environmental justice politics and research. Environmental justice is mostly associated with egalitarianism as the sole justice principle for all people. In contrast, we argue that it is important to uncover and consider heterogeneity in justice concerns to achieve socially accepted solutions to environmental social dilemmas. With noise pollution as an example, we explore citizens’ preferences for justice principles regarding the allocation of politically initiated environmental benefits. In our survey in four European cities, respondents were asked to choose between different outcomes of a program to reduce road traffic noise in line with the following four notions of distributive justice: equal shares, equal outcomes, the greatest benefit for the least advantaged (Rawls), and the greatest benefit for the greatest number (Bentham). We found that most respondents chose Rawls’ principle, a preference that was stable over time but weaker when explicitly introducing the veil of ignorance. The preference for Rawls notwithstanding, we observed substantial heterogeneity in justice preferences. Multinomial logit analyses of survey and geo-referenced data on noise exposure showed that respondents with a higher socio-economic status and lower exposure to traffic noise were more likely to choose Rawls’ principle. Taken together, our study confirms the prominence of Rawls’ principle, demonstrates empirically the heterogeneity of justice preferences, and calls for more direct measurements of such preferences in research on environmental social dilemmas, environmental justice, and beyond. Full article

(This article belongs to the Special Issue Fairness in Non-cooperative Strategic Interactions)

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25 pages, 434 KiB

Open AccessArticle

Strategic Synergies: Unveiling the Interplay of Game Theory and Cultural Dynamics in a Globalized World

by Yufei Wang, Mangirdas Morkūnas and Jinzhao Wei

Games 2024, 15(4), 24; https://doi.org/10.3390/g15040024 - 30 Jun 2024

This literature review focuses on cultural-related studies and game theory. First of all, it analyzes how social dynamics and strategic interactions can be shaped by different cultural environments. Secondly, it examines how cultural norms can affect strategic decision making and how game theory [...] Read more.

This literature review focuses on cultural-related studies and game theory. First of all, it analyzes how social dynamics and strategic interactions can be shaped by different cultural environments. Secondly, it examines how cultural norms can affect strategic decision making and how game theory could predict cooperations and conflicts. Overall, this study aims to highlight the applicability of game theory in the modeling of cultural transformation and its interaction with behavioral economics. Moreover, this study also attempts to underscore the significance of game theory and cultural diversity in communication methods, plus the process of policy formulation. In addition to the above topics, the robustness of cross-cultural social norms, the economic study of different cultural heritage, and the cultural effects of tourism under game theory are also focal points of this study. Finally, this review delves into how game theory can represent social interactions, emphasizing the need to incorporate extensive cultural knowledge in order to enhance the efficacy of game-theoretic model’s applications. Full article

23 pages, 1064 KiB

Open AccessArticle

Payment Systems, Insurance, and Agency Problems in Healthcare: A Medically Framed Real-Effort Experiment

by Manela Karunadasa and Katri K. Sieberg

Games 2024, 15(4), 23; https://doi.org/10.3390/g15040023 - 28 Jun 2024

Background: This study aims to examine the impact of different healthcare payment systems, specifically salary and fee-for-service (FFS) models, on service provision, patient welfare, and quality of care. The influence of payment models on healthcare delivery and patient outcomes, as well as [...] Read more.

Background: This study aims to examine the impact of different healthcare payment systems, specifically salary and fee-for-service (FFS) models, on service provision, patient welfare, and quality of care. The influence of payment models on healthcare delivery and patient outcomes, as well as how these models affect doctors’ decision-making based on patients’ insurance coverage, is not well understood. Methods: A medically framed real-effort task experiment was conducted. This study compared two payment systems: salary and FFS models. Key outcomes measured included the level of service provision, patient welfare, and quality of care. The analysis focused on how financial incentives and patient insurance coverage influenced healthcare decisions. Results: This study found overtreatment in FFS models and undertreatment in salary-based models. Healthcare decisions are significantly influenced by financial incentives and patient needs. Specifically, in FFS models, decisions are driven by self-interest, while in salary models, they are guided by patient needs. Within the FFS model, insurance coverage affects doctors’ decisions and patients’ benefits. Insured patients often receive unnecessary or incorrect procedures, indicating a supply-side moral hazard. Conclusions: Financial incentives and patient insurance coverage significantly influence healthcare decisions, with FFS models promoting self-interested decision-making and salary models focusing more on patient needs. This study contributes to the literature on supply-side moral hazard to health economics studies that use laboratory experiments to model medical decision-making. Full article

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29 pages, 1001 KiB

Open AccessArticle

Fairness and Transparency in One-to-Many Bargaining with Complementarity: An Experimental Study

by Vincent Mak and Rami Zwick

Games 2024, 15(4), 22; https://doi.org/10.3390/g15040022 - 25 Jun 2024

We report an experiment designed to study bargaining behavior between one buyer and multiple sellers with complementarity and how it is influenced by fairness concern and information transparency. We base our setup on a structured alternating-offer bargaining model in which a buyer procures [...] Read more.

We report an experiment designed to study bargaining behavior between one buyer and multiple sellers with complementarity and how it is influenced by fairness concern and information transparency. We base our setup on a structured alternating-offer bargaining model in which a buyer procures complementary items from two heterogeneous sellers with endogenous choice of the order of bargaining. In addition, we implemented an information transparency manipulation regarding whether the sellers were informed about each other’s offers/counteroffers with the buyer. Experimental behavior exhibited deviations from equilibrium predictions that did not differ significantly by information condition, suggesting that sellers were not significantly influenced by direct social comparison between each other. Further analysis suggests that each seller demanded splitting the value of the deal approximately half-half with the buyer as a normative fairness benchmark. The buyers, on the other hand, did not have a demand for fairness that was based on a fairness benchmark. Full article

(This article belongs to the Special Issue Fairness in Non-cooperative Strategic Interactions)

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7 pages, 233 KiB

Open AccessArticle

Collusive Stability with Relative Performance and Network Externalities

by Yi-Shan Lu, Chien-Shu Tsai, Jen-Yao Lee and Chung-Yang Lee

Games 2024, 15(3), 21; https://doi.org/10.3390/g15030021 - 20 Jun 2024

In this paper, we aim to investigate the collusive stability in the presence of network externalities among firms with relative performance in the firm’s objective functions. We demonstrate that collusive stability is increasing (decreasing) in the degree of relative performance, product substitutability and [...] Read more.

In this paper, we aim to investigate the collusive stability in the presence of network externalities among firms with relative performance in the firm’s objective functions. We demonstrate that collusive stability is increasing (decreasing) in the degree of relative performance, product substitutability and network effect when the network effect is sufficiently large (small). A competition agency might need to provide different guidance for anti-competitive regulation in the network industry. Full article

(This article belongs to the Special Issue Industrial Organization and Organizational Economics)

20 pages, 488 KiB

Open AccessArticle

Cheap Talk with Transparent and Monotone Motives from a Seller to an Informed Buyer

by Jeahan Jung and Jeong Yoo Kim

Games 2024, 15(3), 20; https://doi.org/10.3390/g15030020 - 31 May 2024

We develop a model of cheap talk with transparent and monotone motives from a seller to an informed buyer. By transparent and monotone motives, we mean that the seller’s preference does not depend on the state of the world and is increasing in [...] Read more.

We develop a model of cheap talk with transparent and monotone motives from a seller to an informed buyer. By transparent and monotone motives, we mean that the seller’s preference does not depend on the state of the world and is increasing in the choice(s) of the buyer regardless of the state of the world. We first show that if the buyer is completely uninformed, only the babbling equilibrium exists. Then, we obtain our main result that even if the buyer has the slightest information, full revelation can be supported by using the crosschecking strategy of the buyer if and only if the seller has a CARA (constant absolute risk aversion) utility function unless the buyer has too much information. In this equilibrium, the buyer can punish the seller who sends a message far above the buyer’s information by ignoring the seller’s message. Paradoxically, no information and too much information of the buyer both eliminate the fully revealing equilibrium with the crosschecking strategy. We also obtain a counterintuitive result that the seller prefers a more informed buyer than a less informed buyer. Full article

(This article belongs to the Special Issue Communication and Persuasion and Their Economic and Political Applications)

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8 pages, 247 KiB

Open AccessCommunication

A Controlled Discrete-Time Queueing System as a Model for the Orders of Two Competing Companies

by Mario Lefebvre

Games 2024, 15(3), 19; https://doi.org/10.3390/g15030019 - 29 May 2024

We consider two companies that are competing for orders. Let

X_{1} (n)

denote the number of orders processed by the first company at time n, and let

τ (k)

be the first time that [...] Read more.

We consider two companies that are competing for orders. Let

X_{1} (n)

denote the number of orders processed by the first company at time n, and let

τ (k)

be the first time that

X_{1} (n) < j

or

X_{1} (n) = r

, given that

X_{1} (0) = k

. We assume that

{X_{1} (n), n = 0, 1, \dots}

is a controlled discrete-time queueing system. Each company is using some control to increase its share of orders. The aim of the first company is to maximize the expected value of

τ (k)

, while its competitor tries to minimize this expected value. The optimal solution is obtained by making use of dynamic programming. Particular problems are solved explicitly. Full article

(This article belongs to the Section Applied Game Theory)

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25 pages, 963 KiB

Open AccessArticle

Information Transmission and Countervailing Biases in Organizations

by Saori Chiba

Games 2024, 15(3), 18; https://doi.org/10.3390/g15030018 - 22 May 2024

A decision maker (DM) must choose between two projects or decide on no project. The expected benefits of these projects are correlated. The DM seeks advice from an agent with private information about the projects’ benefits. However, the agent’s divergent preferences for projects [...] Read more.

A decision maker (DM) must choose between two projects or decide on no project. The expected benefits of these projects are correlated. The DM seeks advice from an agent with private information about the projects’ benefits. However, the agent’s divergent preferences for projects and lack of consideration for the DM’s implementation costs may introduce two types of biases: project bias, favoring the agent’s project, or pandering bias, favoring the project preferred by the DM. Our findings reveal that project correlation leads to these biases countervailing each other, facilitating the transmission of information. The agent typically recommends a project based on private information to dissuade the DM from choosing no project, as this would be detrimental to the agent. Additionally, we explore optimal delegation within organizations. In contrast to the prevailing literature advocating for delegation to biased agents for enhanced information elicitation, our study suggests limited benefits in the context of project correlation. Full article

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14 pages, 299 KiB

Open AccessArticle

Invariant Equilibrium in Discontinuous Bayesian Games

by Blake A. Allison and Jason J. Lepore

Games 2024, 15(3), 17; https://doi.org/10.3390/g15030017 - 20 May 2024

We provide sufficient conditions on the primitives of a class of discontinuous Bayesian games such that all games in the class share equilibria. If a Bayesian game in the class also satisfies a weak efficiency condition, then we show its normal form is [...] Read more.

We provide sufficient conditions on the primitives of a class of discontinuous Bayesian games such that all games in the class share equilibria. If a Bayesian game in the class also satisfies a weak efficiency condition, then we show its normal form is better-reply secure. The invariance property then provides an existence result for all Bayesian games in the class. Results are shown for both pure strategy and behavioral strategy equilibrium. We illustrate the application of the results with an example of a class of contests with bid caps. Full article

(This article belongs to the Section Non-Cooperative Game Theory)

15 pages, 2987 KiB

Open AccessArticle

Evolution of “Pay-It-Forward” in the Presence of the Temptation to Free-Ride

by Satoshi Uchida, Tatsuya Sasaki, Hitoshi Yamamoto and Isamu Okada

Games 2024, 15(3), 16; https://doi.org/10.3390/g15030016 - 25 Apr 2024

“Paying it forward” is a behavior in which people help someone else because they were helped in the past. Although experimental evidence exists that indicates that real human beings often “pay-it-forward” even in the face of free-rider risks, the theoretical basis for the [...] Read more.

“Paying it forward” is a behavior in which people help someone else because they were helped in the past. Although experimental evidence exists that indicates that real human beings often “pay-it-forward” even in the face of free-rider risks, the theoretical basis for the evolution of this behavior remains unclear. In this paper, we propose a game-theoretical model that explains how pay-it-forward behavior can evolve despite the temptation to free-ride. By assuming that human beings exhibit cognitive distortions, as predicted by prospect theory, and that free-riding is punished with a tiny probability, we demonstrate that pay-it-forward, alongside unconditional altruistic behavior, can evolve and effectively deter free-riding behavior. Full article

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16 pages, 1716 KiB

Open AccessArticle

The Evolution of Cooperation and Diversity under Integrated Indirect Reciprocity

by Tatsuya Sasaki, Satoshi Uchida, Isamu Okada and Hitoshi Yamamoto

Games 2024, 15(2), 15; https://doi.org/10.3390/g15020015 - 18 Apr 2024

Indirect reciprocity is one of the major mechanisms driving the evolution of cooperation in human societies. There are two types of indirect reciprocity: upstream and downstream reciprocity. Cooperation in downstream reciprocity follows the pattern ‘You helped someone, and I will help you’, while [...] Read more.

Indirect reciprocity is one of the major mechanisms driving the evolution of cooperation in human societies. There are two types of indirect reciprocity: upstream and downstream reciprocity. Cooperation in downstream reciprocity follows the pattern ‘You helped someone, and I will help you’, while the direction of cooperation is reversed in upstream reciprocity, which follows the pattern ‘You helped me, and I will help someone else’. These two types of indirect reciprocity often occur in combination. However, upstream and downstream reciprocity have mostly been theoretically studied in isolation. In this study, we propose a new model that integrates both types of reciprocity. In particular, we apply the standard giving-game framework of indirect reciprocity and analyze the three-strategy model including reciprocal altruists, indiscriminate altruists, and free riders using evolutionary game theory. We show that the model allows reciprocal altruists and free riders to coexist stably in well-mixed populations. We also find that by accounting for inattention in the assessment rule, the stability of this mixed equilibrium can be strengthened to prevent the invasion of infamous indiscriminate altruists and can even be made globally stable. Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

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23 pages, 832 KiB

Open AccessArticle

Quid Pro Quo Diplomacy

by Matt Malis and Alastair Smith

Games 2024, 15(2), 14; https://doi.org/10.3390/g15020014 - 17 Apr 2024

Political leaders value public demonstrations of support from foreign leaders and frequently make concessions in order to obtain them. We model the bargaining dynamics surrounding these exchanges and their impact on the recipient leader’s political survival, with a focus on top-level diplomatic visits [...] Read more.

Political leaders value public demonstrations of support from foreign leaders and frequently make concessions in order to obtain them. We model the bargaining dynamics surrounding these exchanges and their impact on the recipient leader’s political survival, with a focus on top-level diplomatic visits as a means of signaling international support. Our model addresses two interrelated questions; first, we consider how symbolic displays of support from one leader to another can be informative even when they are “purchased” with concessions, and second, we derive the equilibrium price and political impact of a visit under different bargaining protocols. The incentive to make a concession in exchange for a visit generally undermines a visit’s signaling value. We identify a diplomatic resource curse, where the existence of opportunities for diplomatic exchange can force leaders into accepting visit-for-concession deals that leave them worse off than if they were diplomatically isolated. Visits never occur when negotiations are fully transparent. Mutually beneficial quid pro quo diplomacy requires opacity in negotiations. Full article

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28 pages, 1953 KiB

Open AccessArticle

Dynamic Awareness and Strategic Adaptation in Cybersecurity: A Game-Theory Approach

by Katarina Kostelić

Games 2024, 15(2), 13; https://doi.org/10.3390/g15020013 - 8 Apr 2024

Cited by 1

Awareness and human factors are becoming ever more important in cybersecurity, particularly in the context of small companies that may need more resources to deal with cybersecurity effectively. This paper introduces a theoretical framework for game analysis of the role of awareness in [...] Read more.

Awareness and human factors are becoming ever more important in cybersecurity, particularly in the context of small companies that may need more resources to deal with cybersecurity effectively. This paper introduces a theoretical framework for game analysis of the role of awareness in strategic interactions between the manager and a hacker. A computable approach is proposed based on Bayesian updating to model awareness in a cybersecurity context. The process of gaining awareness considers the manager’s perception of the properties of the hacker’s actions, game history, and common knowledge. The role of awareness in strategy choices and outcomes is analyzed and simulated, providing insights into decision-making processes for managers and highlighting the need to consider probabilistic assessments of threats and the effectiveness of countermeasures. The accuracy of the initial frequencies plays a significant role in the manager’s success, with aligned frequencies leading to optimal results. Inaccurate information on prior frequencies still outperforms complete uncertainty, emphasizing the value of any available intelligence. However, the results suggest that other awareness modeling approaches are necessary to enhance the manager’s agility and adaptiveness when the prior frequencies do not reflect the immediate attacker’s type, indicating the need for improved intelligence about cyber-attacks and examinations of different awareness modeling approaches. Full article

(This article belongs to the Special Issue Game Theory for Cybersecurity and Privacy)

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12 pages, 1648 KiB

Open AccessArticle

Physics-Informed Graph Neural Operator for Mean Field Games on Graph: A Scalable Learning Approach

by Xu Chen, Shuo Liu and Xuan Di

Games 2024, 15(2), 12; https://doi.org/10.3390/g15020012 - 30 Mar 2024

Mean-field games (MFGs) are developed to model the decision-making processes of a large number of interacting agents in multi-agent systems. This paper studies mean-field games on graphs (

G

-MFGs). The equilibria of

G

-MFGs, namely, mean-field equilibria (MFE), are challenging to solve [...] Read more.

Mean-field games (MFGs) are developed to model the decision-making processes of a large number of interacting agents in multi-agent systems. This paper studies mean-field games on graphs (

G

-MFGs). The equilibria of

G

-MFGs, namely, mean-field equilibria (MFE), are challenging to solve for their high-dimensional action space because each agent has to make decisions when they are at junction nodes or on edges. Furthermore, when the initial population state varies on graphs, we have to recompute MFE, which could be computationally challenging and memory-demanding. To improve the scalability and avoid repeatedly solving

G

-MFGs every time their initial state changes, this paper proposes physics-informed graph neural operators (PIGNO). The PIGNO utilizes a graph neural operator to generate population dynamics, given initial population distributions. To better train the neural operator, it leverages physics knowledge to propagate population state transitions on graphs. A learning algorithm is developed, and its performance is evaluated on autonomous driving games on road networks. Our results demonstrate that the PIGNO is scalable and generalizable when tested under unseen initial conditions. Full article

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39 pages, 480 KiB

Open AccessArticle

Matching with Nonexclusive Contracts

by Daniel Ripperger-Suhler

Games 2024, 15(2), 11; https://doi.org/10.3390/g15020011 - 30 Mar 2024

A variety of empirical papers document the coexistence of exclusive and nonexclusive contracts within a given market across a multitude of industries. However, the theoretical literature has not been able to generate a differentiable model with the coexistence of these contracts. I rectify [...] Read more.

A variety of empirical papers document the coexistence of exclusive and nonexclusive contracts within a given market across a multitude of industries. However, the theoretical literature has not been able to generate a differentiable model with the coexistence of these contracts. I rectify the gap in the literature by developing a theoretical model of two-sided matching, in which principals and agents choose between exclusive and nonexclusive contracts with cost-of-effort inefficiencies. I find that the coexistence of contracts relies on cost-sharing between principals, relative bargaining power, and an endogenous outside option. I also find that the pattern of contracts is monotonic with respect to the type distributions of principals and agents. Full article

(This article belongs to the Special Issue Industrial Organization and Organizational Economics)

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