Journal Description
Games
Games
is a scholarly, peer-reviewed, open access journal of strategic interaction, game theory and decision-making 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 20.6 days after submission; acceptance to publication is undertaken in 5.5 days (median values for papers published in this journal in the first half of 2023).
- 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:
0.9 (2022)
Latest Articles
Game Theoretic Foundations of the Gately Power Measure for Directed Networks
Games 2023, 14(5), 64; https://doi.org/10.3390/g14050064 - 26 Sep 2023
Abstract
We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players—constituting a hierarchical network. The power distribution embedded within a hierarchical network can
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We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players—constituting a hierarchical network. The power distribution embedded within a hierarchical network can be represented through appropriate TU-games. We investigate the properties of these TU-representations and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a core power gauge, investigate the relationship of the Gately with the -measure, and construct an axiomatisation of the Gately measure.
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(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)
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A Game-Theoretic Analysis of Baccara Chemin de Fer, II
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and
Games 2023, 14(5), 63; https://doi.org/10.3390/g14050063 - 25 Sep 2023
Abstract
In a previous paper, we considered several models of the parlor game baccara chemin de fer, including Model B2 (a matrix game) and Model B3 (a matrix game), both of which depend on
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In a previous paper, we considered several models of the parlor game baccara chemin de fer, including Model B2 (a matrix game) and Model B3 (a matrix game), both of which depend on a positive-integer parameter d, the number of decks. The key to solving the game under Model B2 was what we called Foster’s algorithm, which applies to additive matrix games. Here “additive” means that the payoffs are additive in the n binary choices that comprise a player II pure strategy. In the present paper, we consider analogous models of the casino game baccara chemin de fer that take into account the percent commission on Banker (player II) wins, where . Thus, the game now depends not just on the discrete parameter d but also on a continuous parameter . Moreover, the game is no longer zero sum. To find all Nash equilibria under Model B2, we generalize Foster’s algorithm to additive bimatrix games. We find that, with rare exceptions, the Nash equilibrium is unique. We also obtain a Nash equilibrium under Model B3, based on Model B2 results, but here we are unable to prove uniqueness.
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(This article belongs to the Special Issue Computational Game Theory and Its Applications)
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On the Nash Equilibria of a Duel with Terminal Payoffs
Games 2023, 14(5), 62; https://doi.org/10.3390/g14050062 - 21 Sep 2023
Abstract
We formulate and study a two-player duel game as a terminal payoffs stochastic game. Players are standing in place and, in every turn, each may shoot at the other (in other words, abstention is allowed). If
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We formulate and study a two-player duel game as a terminal payoffs stochastic game. Players are standing in place and, in every turn, each may shoot at the other (in other words, abstention is allowed). If shoots ( ), either they hit and kill them (with probability ) or they miss and is unaffected (with probability ). The process continues until at least one player dies; if no player ever dies, the game lasts an infinite number of turns. Each player receives a positive payoff upon killing their opponent and a negative payoff upon being killed. We show that the unique stationary equilibrium is for both players to always shoot at each other. In addition, we show that the game also possesses “cooperative” (i.e., non-shooting) non-stationary equilibria. We also discuss a certain similarity that the duel has to the iterated Prisoner’s Dilemma.
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(This article belongs to the Special Issue Learning and Evolution in Games, 1st Edition)
Open AccessArticle
A Two-Player Resource-Sharing Game with Asymmetric Information
Games 2023, 14(5), 61; https://doi.org/10.3390/g14050061 - 17 Sep 2023
Abstract
This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each
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This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each player has knowledge of the reward realizations of different subsets of the resources. If both players choose the same resource, the reward is divided equally between them, whereas if they choose different resources, each player gains the full reward of the resource. We first implement the iterative best response algorithm to find an -approximate Nash equilibrium for this game. This method of finding a Nash equilibrium may not be desirable when players do not trust each other and place no assumptions on the incentives of the opponent. To handle this case, we solve the problem of maximizing the worst-case expected utility of the first player. The solution leads to counter-intuitive insights in certain special cases. To solve the general version of the problem, we develop an efficient algorithmic solution that combines online convex optimization and the drift-plus penalty technique.
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(This article belongs to the Special Issue Applications of Game Theory with Mathematical Methods)
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Delay to Deal: Bargaining with Indivisibility and Round-Dependent Transfer
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Games 2023, 14(5), 60; https://doi.org/10.3390/g14050060 - 13 Sep 2023
Abstract
We examine a bargaining game in which players cannot make arbitrary offers. Instead, players alternately decide whether to accept or delay, and are rewarded with an indivisible portion and a perishable transfer that depends on the round. Our analysis demonstrates that when the
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We examine a bargaining game in which players cannot make arbitrary offers. Instead, players alternately decide whether to accept or delay, and are rewarded with an indivisible portion and a perishable transfer that depends on the round. Our analysis demonstrates that when the initial transfer is large enough, the subgame perfect Nash equilibrium consists of a finite number of rounds of delay before an agreement is reached. The equilibrium delay is longer when the players are more patient, and when the transfer is initially higher and depreciates slower. Nevertheless, the game’s chaotic characteristic makes it arduous to forecast the exact number of delayed rounds or which player will make the ultimate decision. This game can be applied to many social scenarios, particularly those with exogenous costs.
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(This article belongs to the Section Cooperative Game Theory and Bargaining)
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The Art of Sharing Resources: How to Distribute Water during a Drought Period
Games 2023, 14(5), 59; https://doi.org/10.3390/g14050059 - 25 Aug 2023
Abstract
Water scarcity is a growing problem in many regions worldwide. According to the United Nations, around one-fifth of the world’s population lives in areas where water is scarce. Another one-quarter of the world’s population has to face water supply cuts, mainly because this
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Water scarcity is a growing problem in many regions worldwide. According to the United Nations, around one-fifth of the world’s population lives in areas where water is scarce. Another one-quarter of the world’s population has to face water supply cuts, mainly because this proportion of the population lacks the necessary infrastructure to acquire water from rivers and aquifers (UN, 2005). Water is a resource that is essential to human survival and is also present in all productive processes in the economy. Therefore, we are challenged to adequately manage water to ensure the population’s well-being and to achieve socioeconomic development. Specifically, this paper analyzes the situation present in the summer of 2022 at Riudecanyes (a village in Catalonia, Spain), where a drought problem exists. We propose applying the conflicting claims problem theory to give possible solutions to distribute the water. We propose to use this theory to describe the distribution of the available irrigation hours in 2022, considering the demand made by the farmers in the previous year, when there was regular irrigation.
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(This article belongs to the Special Issue Game Theory with Applications to Economics)
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Border Games: A Game Theoretic Model of Undocumented Immigration
by
and
Games 2023, 14(5), 58; https://doi.org/10.3390/g14050058 - 24 Aug 2023
Abstract
We consider a game-theoretic model of undocumented immigration with the aim of emphasizing the strategic interaction between the different forces affecting the issue. Specifically, we analyze the strategic interaction between firms in the destination country, native labor, the elected officials in the destination
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We consider a game-theoretic model of undocumented immigration with the aim of emphasizing the strategic interaction between the different forces affecting the issue. Specifically, we analyze the strategic interaction between firms in the destination country, native labor, the elected officials in the destination country, and the undocumented immigrants from the Source Country. We show that the impact of border enforcement is dampened because strategic interaction between the players will tend to mute any unilateral changes. We also study the effect of uncertainty in the labor market on migration issues and analyze the two cases where policymakers have to make their decisions before (ex-ante) or after (ex-post) the market state is realized.
Full article
(This article belongs to the Special Issue Game Theory Applications to Socio-Environmental Studies, Development Economics and Sustainability Research)
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Open AccessArticle
Fair Allocation in Crowd-Sourced Systems
Games 2023, 14(4), 57; https://doi.org/10.3390/g14040057 - 15 Aug 2023
Abstract
In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. We use the framework of a Shapley allocation which is regarded as
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In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. We use the framework of a Shapley allocation which is regarded as a fundamental method of computing the fair share of all participants in a cooperative game when the values of all possible coalitions could be quantified. To quantify the value of all coalitions, we define a class of value functions for crowd-sourced systems which capture the contributions of the founders and the crowd plausibly and derive closed-form expressions for Shapley allocations to both. These value functions are defined for different scenarios, such as the presence of oligopolies or geographic spread of the crowd, taking network effects, including Metcalfe’s law, into account. A key result we obtain is that under quite general conditions, the crowd participants are collectively owed a share between and of the total value of the crowd-sourced system. We close with an empirical analysis demonstrating the consistency of our results with the compensation offered to the crowd participants in some public internet content sharing companies.
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(This article belongs to the Special Issue Computational Social Choice: Theory and Applications)
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Duopoly and Endogenous Single Product Quality Strategies
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Games 2023, 14(4), 56; https://doi.org/10.3390/g14040056 - 15 Aug 2023
Abstract
This research paper investigates a duopolistic market characterized by vertical product differentiation. The study considers both product qualities and consumer preferences represented as one-dimensional intervals. The focus is on analyzing the equilibrium in a duopoly game with convex production costs. In this setting,
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This research paper investigates a duopolistic market characterized by vertical product differentiation. The study considers both product qualities and consumer preferences represented as one-dimensional intervals. The focus is on analyzing the equilibrium in a duopoly game with convex production costs. In this setting, each firm has the option to present a multi-product strategy consisting of quality–price pairs, and their profits are determined by the decisions made by consumers. The findings of the study reveal that, under typical consumer preference conditions, both firms tend to offer a single quality–price pair. Additionally, the market is shown to be fully served, and firm profits decrease as the index of product quality increases. A comparative analysis is also conducted with the case of a monopoly.
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(This article belongs to the Special Issue Applications of Game Theory to Industrial Organization)
Open AccessArticle
Asymmetric Reimbursement and Contingent Fees in Environmental Conflicts: Observable vs. Unobservable Contracts
by
and
Games 2023, 14(4), 55; https://doi.org/10.3390/g14040055 - 28 Jul 2023
Abstract
We investigate the impact of observability of contracts between a plaintiff and his attorney on both the efficiency of the environmental conflict and the fairness of the resulting outcome from the environmental conflict. By including two specific game-theoretic models (an observable-contract game and
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We investigate the impact of observability of contracts between a plaintiff and his attorney on both the efficiency of the environmental conflict and the fairness of the resulting outcome from the environmental conflict. By including two specific game-theoretic models (an observable-contract game and an unobservable-contract game), we find two key results: (i) The unobservability of a contract may increase inefficiency of the environmental conflict in terms of legal efforts; however, (ii) the unobservability of a contract may increase the fairness of the outcome in terms of the plaintiff’s probability of winning the contest.
Full article
(This article belongs to the Special Issue Fairness in Non-cooperative Strategic Interactions)
Open AccessCommunication
Stackelberg Social Equilibrium in Water Markets
by
and
Games 2023, 14(4), 54; https://doi.org/10.3390/g14040054 - 11 Jul 2023
Abstract
Market power in water markets can be modeled as simultaneous quantity competition on a river structure and analyzed by applying social equilibrium. In an example of a duopoly water market, we argue that the lack of backward induction logic implies that the upstream
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Market power in water markets can be modeled as simultaneous quantity competition on a river structure and analyzed by applying social equilibrium. In an example of a duopoly water market, we argue that the lack of backward induction logic implies that the upstream supplier foregoes profitable strategic manipulation of water to the downstream supplier. To incorporate backward induction, we propose the Stackelberg social equilibrium concept. We prove the existence of Stackelberg social equilibrium in duopoly water markets with an upstream–downstream river structure and derive it in the example of a duopoly market.
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(This article belongs to the Special Issue Game Theory with Applications to Economics)
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Price and Quantity Competition under Vertical Pricing
Games 2023, 14(4), 53; https://doi.org/10.3390/g14040053 - 29 Jun 2023
Abstract
We consider a vertically related market where one quantity-setting and another price-setting downstream firm negotiate the terms of a two-part tariff contract with an upstream input supplier. In contrast to the traditional belief, we show that the price-setting firm produces a higher output
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We consider a vertically related market where one quantity-setting and another price-setting downstream firm negotiate the terms of a two-part tariff contract with an upstream input supplier. In contrast to the traditional belief, we show that the price-setting firm produces a higher output and earns a higher profit than the quantity-setting firm when bargaining is decentralised. Additionally, both firms produce the same output, whereas the profit is higher under the price-setting firm than the quantity-setting firm when bargaining is centralised.
Full article
(This article belongs to the Special Issue Applications of Game Theory to Industrial Organization)
Open AccessArticle
Evasion Differential Game of Multiple Pursuers and a Single Evader with Geometric Constraints in ℓ2
Games 2023, 14(4), 52; https://doi.org/10.3390/g14040052 - 29 Jun 2023
Abstract
We investigate a differential evasion game with multiple pursuers and an evader for the infinite systems of differential equations in ℓ2. The control functions of the players are subject to geometric constraints. The pursuers’ goal is to bring the state of
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We investigate a differential evasion game with multiple pursuers and an evader for the infinite systems of differential equations in ℓ2. The control functions of the players are subject to geometric constraints. The pursuers’ goal is to bring the state of at least one of the controlled systems to the origin of ℓ2, while the evader’s goal is to prevent this from happening in a finite interval of time. We derive a sufficient condition for evasion from any initial state and construct an evasion strategy for the evader.
Full article
(This article belongs to the Special Issue Applications of Differential Game and Its Related Theories in Mathematics and Economics)
Open AccessArticle
Power Indices under Specific Multicriteria Status
Games 2023, 14(4), 51; https://doi.org/10.3390/g14040051 - 27 Jun 2023
Abstract
By considering the maximal efficacy among allocation vectors, we define two power indices under specific multicriteria conditions. Additionally, we introduce a reduction approach to the axiomatic framework for these power indices. Furthermore, we propose an alternative formulation that focuses on discrepancy mapping. Based
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By considering the maximal efficacy among allocation vectors, we define two power indices under specific multicriteria conditions. Additionally, we introduce a reduction approach to the axiomatic framework for these power indices. Furthermore, we propose an alternative formulation that focuses on discrepancy mapping. Based on reduction and discrepancy mapping, we also provide two dynamic procedures.
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(This article belongs to the Special Issue Advances in Game Theory, Multi-Agent Systems, and Computer Security)
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Some Properties of Interval Shapley Values: An Axiomatic Analysis
by
and
Games 2023, 14(3), 50; https://doi.org/10.3390/g14030050 - 15 Jun 2023
Abstract
Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval instead of a real number. This study revisits two interval game versions of Shapley values (i.e., the interval
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Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval instead of a real number. This study revisits two interval game versions of Shapley values (i.e., the interval Shapley value and the interval Shapley-like value) and characterizes them using an axiomatic approach. For the interval Shapley value, we show that the existing axiomatization can be generalized to a wider subclass of interval games called size monotonic games. For the interval Shapley-like value, we show that a standard axiomatization using Young’s strong monotonicity holds on the whole class of interval games.
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(This article belongs to the Section Cooperative Game Theory and Bargaining)
Open AccessArticle
Gender and Risk Aversion: Evidence from a Natural Experiment
Games 2023, 14(3), 49; https://doi.org/10.3390/g14030049 - 14 Jun 2023
Abstract
The theoretical literature on risk aversion and Expected Utility Theory is extensive; however, the analysis of this behaviour with natural experiments could be more comprehensive. In this paper, we use data from 120 episodes of the Portuguese version of the TV game show
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The theoretical literature on risk aversion and Expected Utility Theory is extensive; however, the analysis of this behaviour with natural experiments could be more comprehensive. In this paper, we use data from 120 episodes of the Portuguese version of the TV game show The Price is Right, namely from The Wheel game, to explore risk aversion as well as the impact of gender in decision-making. The Wheel game has straightforward rules and huge expected payoffs. All contestants have access to the same information and distributions of uncertainty, making it a unique field laboratory to conduct an experimental test of rational decision theory. The objective is to infer the risk aversion levels of decision-makers from their choice to turn the wheel and the influence of gender on risk attitudes. There is a widespread view that women are more risk-averse than men. However, we could not reject the hypothesis that women and men have the same level of risk aversion. Nevertheless, we have evidence that contestants are more risk-averse than risk-seeking. The omission bias, loss aversion and regret can explain that behaviour.
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Open AccessArticle
Optimal Contest Design When Policing Damaging Behavior
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Games 2023, 14(3), 48; https://doi.org/10.3390/g14030048 - 13 Jun 2023
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We consider the design of a contest in which the prize may motivate not only productive efforts, but also some damaging aggressive behavior by contestants. The organizer must choose prizes and an enforcement regime defined as a limit on how much aggressiveness will
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We consider the design of a contest in which the prize may motivate not only productive efforts, but also some damaging aggressive behavior by contestants. The organizer must choose prizes and an enforcement regime defined as a limit on how much aggressiveness will be tolerated and the probability of inspection. When the value of contestants’ output is low, it may be optimal to motivate much less effort than first best because the prize spread necessary to induce higher effort necessitates a high level of enforcement, which is not worth the cost. On the other hand, when the output value is sufficiently high, it becomes optimal to offer a high prize spread to motivate substantial but still below first-best effort, with costly enforcement then being employed to constrain damaging aggressive behavior. Additionally, a less accurate inspection technology is associated with a tighter limit on aggressive behavior, and “zero tolerance” can be optimal if the aggressive behavior has no value.
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Open AccessArticle
Simple Mediation in a Cheap-Talk Game
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Games 2023, 14(3), 47; https://doi.org/10.3390/g14030047 - 02 Jun 2023
Abstract
In the Crawford–Sobel (uniform, quadratic utility) cheap-talk model, we consider a simple mediation scheme (a communication device) in which the informed agent reports one of the N possible elements of a partition to the mediator and then the mediator suggests one of the
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In the Crawford–Sobel (uniform, quadratic utility) cheap-talk model, we consider a simple mediation scheme (a communication device) in which the informed agent reports one of the N possible elements of a partition to the mediator and then the mediator suggests one of the N actions to the uninformed decision-maker according to the probability distribution of the device. We show that no such simple mediated equilibrium can improve upon the unmediated N-partition Crawford–Sobel equilibrium when the preference divergence parameter (bias) is small.
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Open AccessArticle
Payment Systems, Supplier-Induced Demand, and Service Quality in Credence Goods: Results from a Laboratory Experiment
Games 2023, 14(3), 46; https://doi.org/10.3390/g14030046 - 31 May 2023
Abstract
This experiment examines the relationship between payment systems and the quality and quantity of services provided in credence goods markets. By using a real-effort task to stimulate the decision making of service providers, the study finds that payment systems do indeed have an
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This experiment examines the relationship between payment systems and the quality and quantity of services provided in credence goods markets. By using a real-effort task to stimulate the decision making of service providers, the study finds that payment systems do indeed have an impact on service provision. Specifically, providers in fee-for-service systems over-provide, while those in salary systems under-provide services. Additionally, there is a lack of alignment between the services provided under fee-for-service and the actual needs of customers, resulting in a substantial loss of customer benefits under fee-for-service in comparison to under salary. The study also finds that providers in fee-for-service systems perform more faulty tasks than those in salary, indicating that they may prioritize quantity over quality in their services. As for insurance, the results of this study show no significant effect of insurance on the number of services provided; however, customers without insurance received significantly more faulty tasks. Based on these results, the study concludes that payment systems play an important role in determining the quality and quantity of services provided in credence goods markets. Overall, this study highlights the need for a better alignment between customer needs and services provided under fee-for-service systems.
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(This article belongs to the Special Issue Competition, Coordination, and Cooperation: Theory and Evidence)
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Correlated Equilibrium and Evolutionary Stability in 3-Player Rock-Paper-Scissors
Games 2023, 14(3), 45; https://doi.org/10.3390/g14030045 - 30 May 2023
Abstract
In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner
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In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner outcomes than would result from the Nash equilibrium. The correlated equilibrium is evolutionarily stable because any mutant fares worse than a signal-following player when facing two players who follow their own correlated signals. The critical quality of the correlation device is to make this true both for potential mutants who would disobey their signal and instead choose the action which would beat the action signaled to the player, as well as for potential mutants who would deviate to the action that would be beaten by what the device signals to the player. These findings reveal how a strict correlated equilibrium can produce evolutionarily stable strategies for rock-paper-scissors with three players.
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(This article belongs to the Section Non-Cooperative Game Theory)
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Special Issue in
Games
In Pursuit of the Unification of Evolutionary Dynamics
Guest Editors: Arnaud Z. Dragicevic, Ştefan Cristian GherghinaDeadline: 30 September 2023
Special Issue in
Games
Game Theory Applications to Socio-Environmental Studies, Development Economics and Sustainability Research
Guest Editors: Elkhan Richard Sadik-Zada, Andrea Gatto, Luigi Aldieri, Giovanna Bimonte, Luigi Senatore, Concetto Paolo VinciDeadline: 30 November 2023
Special Issue in
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Evolution of Cooperation and Evolutionary Game Theory
Guest Editors: Qi Su, Alberto AntonioniDeadline: 31 December 2023