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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 19.1 days after submission; acceptance to publication is undertaken in 6.7 days (median values for papers published in this journal in the second half of 2022).
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.

Imprint Information Journal Flyer Open Access ISSN: 2073-4336

Latest Articles

Open AccessArticle

Payment Systems, Supplier-Induced Demand, and Service Quality in Credence Goods: Results from a Laboratory Experiment

by

Manela Karunadasa

,

Katri K. Sieberg

and

Toni Tapani Kristian Jantunen

Games 2023, 14(3), 46; https://doi.org/10.3390/g14030046 - 31 May 2023

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Competition, Coordination, and Cooperation: Theory and Evidence)

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Open AccessArticle

Correlated Equilibrium and Evolutionary Stability in 3-Player Rock-Paper-Scissors

by

William C. Grant

Games 2023, 14(3), 45; https://doi.org/10.3390/g14030045 - 30 May 2023

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 [...] Read more.

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. Full article

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

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Open AccessArticle

Training, Abilities and the Structure of Teams

by

Games 2023, 14(3), 44; https://doi.org/10.3390/g14030044 - 26 May 2023

Training in firms has an effect on the productivity of employees who receive the training, and depending on the production technology, on the other employees as well. Meanwhile, changing the remuneration structure within a team can change the stability of a team. In [...] Read more.

Training in firms has an effect on the productivity of employees who receive the training, and depending on the production technology, on the other employees as well. Meanwhile, changing the remuneration structure within a team can change the stability of a team. In this paper, we apply the production games approach of cooperative game theory to analyze how training employees affects the stability of team structures and employee wages. Concretely, we apply coalition structures and the

χ

value. Our results are in line with the literature and numerous further research questions can be addressed based on our approach. Full article

(This article belongs to the Special Issue Applications of Game Theory to Industrial Organization)

Open AccessArticle

Strategic Information Suppression in Borrowing and Pre-Lending Cognition: Theory and Evidence

by

and

Games 2023, 14(3), 43; https://doi.org/10.3390/g14030043 - 24 May 2023

This paper theoretically studies the interaction between an informed borrower and an uninformed lender facing possible default of a loan application. The lender is motivated to invest cognitive resources before making a lending decision. If the regulatory fine is weak, it is impossible [...] Read more.

This paper theoretically studies the interaction between an informed borrower and an uninformed lender facing possible default of a loan application. The lender is motivated to invest cognitive resources before making a lending decision. If the regulatory fine is weak, it is impossible for a bad-debt borrower to fully disclose his situation in the application. In this case, when the likelihood of a bad debt is low, the borrower always claims that nothing in the application is wrong. Otherwise, the borrower randomizes between full disclosure and information suppression. The transaction cost of the lender’s pre-lending cognition increases with the default probability, as the default probability is small and decreases thereafter. Evidence from a peer-to-peer lending platform with 816,274 observations between 2012 and 2015 in the United States is largely consistent with our model implications. Full article

(This article belongs to the Special Issue Economics of Motivated Beliefs)

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Open AccessArticle

Invasion of Optimal Social Contracts

by

Alessandra F. Lütz

,

Marco Antonio Amaral

,

and

Games 2023, 14(3), 42; https://doi.org/10.3390/g14030042 - 15 May 2023

The stag-hunt game is a prototype for social contracts. Adopting a new and better social contract is usually challenging because the current one is already well established and stable due to sanctions imposed on non-conforming members. Thus, how does a population shift from [...] Read more.

The stag-hunt game is a prototype for social contracts. Adopting a new and better social contract is usually challenging because the current one is already well established and stable due to sanctions imposed on non-conforming members. Thus, how does a population shift from the current social contract to a better one? In other words, how can a social system leave a locally optimum configuration to achieve a globally optimum state? Here, we investigate the effect of promoting diversity on the evolution of social contracts. We consider group-structured populations where individuals play the stag-hunt game in all groups. We model the diversity incentive as a snowdrift game played in a single focus group where the individual is more prone to adopting a deviant norm. We show that a moderate diversity incentive is sufficient to change the system dynamics, driving the population over the stag-hunt invasion barrier that prevents the global optimum being reached. Thus, an initial fraction of adopters of the new, better norm can drive the system toward the optimum social contract. If the diversity incentive is not too large, the better social contract is the new equilibrium and remains stable even if the incentive is turned off. However, if the incentive is large, the population is trapped in a mixed equilibrium and the better social norm can only be reached if the incentive is turned off after the equilibrium is reached. The results are obtained using Monte Carlo simulations and analytical approximation methods. Full article

(This article belongs to the Special Issue In Pursuit of the Unification of Evolutionary Dynamics)

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Open AccessArticle

Social Learning for Sequential Driving Dilemmas

by

,

and

Games 2023, 14(3), 41; https://doi.org/10.3390/g14030041 - 11 May 2023

Autonomous driving (AV) technology has elicited discussion on social dilemmas where trade-offs between individual preferences, social norms, and collective interests may impact road safety and efficiency. In this study, we aim to identify whether social dilemmas exist in AVs’ sequential decision making, which [...] Read more.

Autonomous driving (AV) technology has elicited discussion on social dilemmas where trade-offs between individual preferences, social norms, and collective interests may impact road safety and efficiency. In this study, we aim to identify whether social dilemmas exist in AVs’ sequential decision making, which we call “sequential driving dilemmas” (SDDs). Identifying SDDs in traffic scenarios can help policymakers and AV manufacturers better understand under what circumstances SDDs arise and how to design rewards that incentivize AVs to avoid SDDs, ultimately benefiting society as a whole. To achieve this, we leverage a social learning framework, where AVs learn through interactions with random opponents, to analyze their policy learning when facing SDDs. We conduct numerical experiments on two fundamental traffic scenarios: an unsignalized intersection and a highway. We find that SDDs exist for AVs at intersections, but not on highways. Full article

(This article belongs to the Special Issue Learning and Evolution in Games I)

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Open AccessArticle

First You Get the Money, Then You Get the Power: The Effect of Cheating on Altruism

by

David B. Johnson

and

Jonathan Rogers

Games 2023, 14(3), 40; https://doi.org/10.3390/g14030040 - 04 May 2023

When there is direct competition for a position of power (promotion, elected office, etc.), competitors are tempted to cheat to increase their chances of winning. If they do so successfully, then how they rationalize their cheating can determine how they treat the losers [...] Read more.

When there is direct competition for a position of power (promotion, elected office, etc.), competitors are tempted to cheat to increase their chances of winning. If they do so successfully, then how they rationalize their cheating can determine how they treat the losers of the competition. In this paper, we explore how the winners of a promotion tournament treat the losers, using a two stage laboratory experiment run in Canada and the United Arab Emirates. In the first stage, subjects compete to earn the role of the dictator in a dictator game, which takes place in the second stage. We vary whether or not subjects can cheat during the competition. The results of the experiment can be summarized as follows: (1) cheating significantly increases altruism in some tournament winners, (2) winners who cheat the most are significantly less altruistic than winners who cheated only a little, (3) there are significant differences in cheating behavior across the two populations, and (4) cheating behavior can be at least partially attributed to differences in intelligence and beliefs across the two populations. Full article

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Open AccessArticle

On Some Connections between Negotiating while Fighting and Bargaining between a Buyer and Seller

by

Games 2023, 14(3), 39; https://doi.org/10.3390/g14030039 - 28 Apr 2023

We point out an equivalence between a class of games in which players negotiate while fighting and a class of games in which a buyer and seller negotiate over terms. Importantly and perhaps ironically, bargaining before fighting is strategically distinct from bargaining before [...] Read more.

We point out an equivalence between a class of games in which players negotiate while fighting and a class of games in which a buyer and seller negotiate over terms. Importantly and perhaps ironically, bargaining before fighting is strategically distinct from bargaining before a change of ownership but bargaining while fighting is equivalent to bargaining before a change of ownership. These connections and intuition from models of bilateral trade help shed light on two mechanisms for learning while frighting: inference based on observing strategic choices and information leakage on the battlefield. Debates on the relative importance of these to mechanism are addressed; some subtle clarifications to extant arguments are provided. Moreover, the importance of learning hard information from the battlefield is connected to work on Coasian Dynamics with information leakage and avenuse for future work relying on advances in behavioral theory are sketched out. Full article

(This article belongs to the Special Issue Negotiations: The Good, the Bad, and the Ugly)

Open AccessArticle

Time-Inconsistent Bargaining and Cross-Commitments

by

Manuel A. Utset

Games 2023, 14(3), 38; https://doi.org/10.3390/g14030038 - 28 Apr 2023

The paper studies bargaining games involving players with present-biased preferences. The paper shows that the relative timing of bargaining rewards and bargaining costs will determine whether the players’ present-bias will affect bargaining outcomes. In cases where players agree to a bargain in period [...] Read more.

The paper studies bargaining games involving players with present-biased preferences. The paper shows that the relative timing of bargaining rewards and bargaining costs will determine whether the players’ present-bias will affect bargaining outcomes. In cases where players agree to a bargain in period 1 and experience all bargaining payoffs in period 2, the players will act in a time-consistent fashion. When time-inconsistent players incur immediate bargaining costs to produce delayed rewards, they will have an incentive to procrastinate. On the other hand, when players receive immediate bargaining rewards and incur delayed costs, they will have incentives to agree to bargains too soon and to agree to inefficient bargains. The paper shows that the players’ awareness of their own and the other player’s present-biased preferences will determine whether they engage in repeated time-inconsistent bargaining. A naïve player who engages in time-inconsistent bargaining will suffer welfare losses. We show that time-inconsistent bargaining can also create spillover welfare losses for other players. A time-consistent player who is counterparty-naïve about the other player can suffer spillover welfare losses that can be higher than those incurred by the time-inconsistent player. As a result, counterparty-sophisticated players will have an incentive to use cross-commitment devices to reduce the likelihood of spillover welfare losses. The paper also shows that cross commitment devices that target immediate payoffs dominate cross-commitments that target delayed payoffs. Finally, the paper shows that time-inconsistent bargaining can lead to inefficient delays in agreeing to bargains and in exiting bargaining relationships. Full article

(This article belongs to the Special Issue Negotiations: The Good, the Bad, and the Ugly)

Open AccessArticle

Fighting for Routes: Resource Allocation among Competing Planners in Transportation Networks

by

Charlotte Roman

and

Games 2023, 14(3), 37; https://doi.org/10.3390/g14030037 - 28 Apr 2023

In transportation networks, incomplete information is ubiquitous, and users often delegate their route choice to distributed route planners. To model and study these systems, we introduce network control games, consisting of multiple actors seeking to optimise the social welfare of their assigned subpopulations [...] Read more.

In transportation networks, incomplete information is ubiquitous, and users often delegate their route choice to distributed route planners. To model and study these systems, we introduce network control games, consisting of multiple actors seeking to optimise the social welfare of their assigned subpopulations through resource allocation in an underlying nonatomic congestion game. We first analyse the inefficiency of the routing equilibria by calculating the Price of Anarchy for polynomial cost functions, and then, using an Asynchronous Advantage Actor–Critic algorithm implementation, we show that reinforcement learning agents are vulnerable to choosing suboptimal routing as predicted by the theory. Finally, we extend the analysis to allow vehicles to choose their route planner and study the associated equilibria. Our results can be applied to mitigate inefficiency issues arising in large transport networks with route controlled autonomous vehicles. Full article

(This article belongs to the Special Issue Negotiations: The Good, the Bad, and the Ugly)

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Open AccessArticle

Improving Strategic Decisions in Sequential Games by Exploiting Positional Similarity

by

and

Games 2023, 14(3), 36; https://doi.org/10.3390/g14030036 - 28 Apr 2023

We study the strategic similarity of game positions in two-player extensive games of perfect information by looking at the structure of their local game trees, with the aim of improving the performance of game-playing agents in detecting forcing continuations. We present a range [...] Read more.

We study the strategic similarity of game positions in two-player extensive games of perfect information by looking at the structure of their local game trees, with the aim of improving the performance of game-playing agents in detecting forcing continuations. We present a range of measures over the induced game trees and compare them against benchmark problems in chess, observing a promising level of accuracy in matching up trap states. Our results can be applied to chess-like interactions where forcing moves play a role, such as those arising in bargaining and negotiation. Full article

(This article belongs to the Special Issue Negotiations: The Good, the Bad, and the Ugly)

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Open AccessArticle

The Role of the Status-Quo in Dynamic Bargaining

by

Francesca Flamini

Games 2023, 14(3), 35; https://doi.org/10.3390/g14030035 - 28 Apr 2023

We analyze a dynamic bargaining game where parties can agree to implement a policy change, which is costly (beneficial) in the short-run but beneficial (costly) in the long-run. When the status-quo is endogenized (at least in some components), we show that the more [...] Read more.

We analyze a dynamic bargaining game where parties can agree to implement a policy change, which is costly (beneficial) in the short-run but beneficial (costly) in the long-run. When the status-quo is endogenized (at least in some components), we show that the more farsighted party can induce their rival to accept the short-run costs of policy changes designed to generate benefits in the long-run. This is more common when players’ asymmetries are less pronounced, the status-quo is fully endogenized and the state depreciates more quickly. Full article

(This article belongs to the Special Issue Negotiations: The Good, the Bad, and the Ugly)

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Open AccessArticle

Blockchain-Based Dispute Resolution: Insights and Challenges

by

Yannick Gabuthy

Games 2023, 14(3), 34; https://doi.org/10.3390/g14030034 - 28 Apr 2023

A smart contract can be defined as a computer program, stored on a blockchain, which allows a transaction or an agreement—defined ex-ante—to be self-executed when some conditions are met, and without the need for a central authority to enforce it. Even if [...] Read more.

A smart contract can be defined as a computer program, stored on a blockchain, which allows a transaction or an agreement—defined ex-ante—to be self-executed when some conditions are met, and without the need for a central authority to enforce it. Even if this new technology is very promising, it may face a challenge: the codified nature of smart contracts creates new types of disputes that require new mechanisms of dispute resolution, which are precisely based on the blockchain. The aim of this article is to analyze one of these emerging mechanisms, namely Kleros, which is a blockchain-based dispute resolution platform implying crowdsourced jurors whose incentives to make fair decisions are based on game theory. The Kleros case provides also a basis for a broader discussion on the future of the decentralized justice market. Full article

(This article belongs to the Special Issue Negotiations: The Good, the Bad, and the Ugly)

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Open AccessArticle

A Differential Game for Optimal Water Price Management

by

Andrea Caravaggio

,

Luigi De Cesare

and

Andrea Di Liddo

Games 2023, 14(2), 33; https://doi.org/10.3390/g14020033 - 05 Apr 2023

This article studies a leader–follower differential game with a finite horizon, where a single buyer reacts to the selling price set by an agency (water supplier). The Open-Loop Stackelberg equilibrium is calculated, assuming that the user demand is fully satisfied (that is, the [...] Read more.

This article studies a leader–follower differential game with a finite horizon, where a single buyer reacts to the selling price set by an agency (water supplier). The Open-Loop Stackelberg equilibrium is calculated, assuming that the user demand is fully satisfied (that is, the interior solution is considered), and the following different tariff schemes are analyzed: linear scheme, increasing block tariff, and convex tariff. Numerical simulations highlight how tariff convexity and seasonality in buyer’s preferences affect water price and demand, and the dynamics of the basin over time. The study shows that synchrony or asynchrony between basin recharge and buyer cyclical demand can dramatically affect the dynamics and basin levels observed at the end of the time period considered. Additionally, the presence of a large number of fluctuations in buyer preferences affects basin fluctuations, while natural recharge may help in maintaining acceptable levels of future water demands. 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

Measuring the Difficulties in Forming a Coalition Government

by

Games 2023, 14(2), 32; https://doi.org/10.3390/g14020032 - 31 Mar 2023

Electoral thresholds in the context of parliamentary elections are an instrument for preventing the fragmentation of parliaments and facilitate the formation of a coalition government. However, the clauses also introduce distortions and modify the equality of electoral votes in an election. In order [...] Read more.

Electoral thresholds in the context of parliamentary elections are an instrument for preventing the fragmentation of parliaments and facilitate the formation of a coalition government. However, the clauses also introduce distortions and modify the equality of electoral votes in an election. In order to decide to what extent these negative effects can be accepted, it is necessary to measure the difficulties in forming a coalition government and to quantify the effects of electoral thresholds on these difficulties. For this issue, we introduce a concept based on cooperative game theory which takes into account the distribution of seats in parliament and coalition statements of parties. Full article

(This article belongs to the Section Applied Game Theory)

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Open AccessArticle

Equivalent Modes of Reimbursement in Augmented Contests

by

,

and

Games 2023, 14(2), 31; https://doi.org/10.3390/g14020031 - 31 Mar 2023

This article presents an equivalence theorem in the context of Tullock’s augmented lottery contest with external or internal cost reimbursement. Three alternative modes of reimbursement are studied. The equivalence implies that, even though the augmented contest is vulnerable to framing biases, it is [...] Read more.

This article presents an equivalence theorem in the context of Tullock’s augmented lottery contest with external or internal cost reimbursement. Three alternative modes of reimbursement are studied. The equivalence implies that, even though the augmented contest is vulnerable to framing biases, it is strategically neutral. Full article

Open AccessArticle

Robust Satisfaction of Metric Interval Temporal Logic Objectives in Adversarial Environments

by

,

Bhaskar Ramasubramanian

,

and

Radha Poovendran

Games 2023, 14(2), 30; https://doi.org/10.3390/g14020030 - 30 Mar 2023

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in the presence of an adversary. The time-sensitive task is specified as a formula in the metric interval temporal logic (MITL). CPSs that [...] Read more.

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in the presence of an adversary. The time-sensitive task is specified as a formula in the metric interval temporal logic (MITL). CPSs that operate in adversarial environments have typically been abstracted as stochastic games (SGs); however, because traditional SG models do not incorporate a notion of time, they cannot be used in a setting where the objective is time-sensitive. To address this, we introduce durational stochastic games (DSGs). DSGs generalize SGs to incorporate a notion of time and model the adversary’s abilities to tamper with the control input (actuator attack) and manipulate the timing information that is perceived by the CPS (timing attack). We define notions of spatial, temporal, and spatio-temporal robustness to quantify the amounts by which system trajectories under the synthesized policy can be perturbed in space and time without affecting satisfaction of the MITL objective. In the case of an actuator attack, we design computational procedures to synthesize controllers that will satisfy the MITL task along with a guarantee of its robustness. In the presence of a timing attack, we relax the robustness constraint to develop a value iteration-based procedure to compute the CPS policy as a finite-state controller to maximize the probability of satisfying the MITL task. A numerical evaluation of our approach is presented on a signalized traffic network to illustrate our results. Full article

(This article belongs to the Special Issue Game-Theoretic Analysis of Network Security and Privacy)

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Open AccessArticle

Network Externalities and Downstream Collusion under Asymmetric Costs: A Note

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and

Games 2023, 14(2), 29; https://doi.org/10.3390/g14020029 - 30 Mar 2023

This paper considers the collusive stability of downstream competition in a vertical market with network externalities and cost asymmetry. A dynamic collusion game is constructed, and backward induction is employed to solve the subgame perfect Nash equilibrium. We show that larger network externalities [...] Read more.

This paper considers the collusive stability of downstream competition in a vertical market with network externalities and cost asymmetry. A dynamic collusion game is constructed, and backward induction is employed to solve the subgame perfect Nash equilibrium. We show that larger network externalities lead to less collusive incentive for an inefficient firm, while for an efficient firm, this depends on the efficiency gap. An increase in network externalities will destabilize the downstream collusion when the cost asymmetry is large and network externalities are relatively weak. Full article

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Open AccessEditorial

A Yin and Yang Perspective on the Trust Game: Trust and Reciprocity

by

Games 2023, 14(2), 28; https://doi.org/10.3390/g14020028 - 23 Mar 2023

Trust and reciprocity are fundamental for the cohesion and stability of human society, as they are essential components of cooperative exchange [...] Full article

(This article belongs to the Special Issue A Yin and Yang Perspective on the Trust Game: Trust and Reciprocity)

Open AccessEditorial

Advances in the Theory and Applications of Contests and Tournaments: Introduction to the Special Issue

by

Theofanis Tsoulouhas

Games 2023, 14(2), 27; https://doi.org/10.3390/g14020027 - 17 Mar 2023

The theory of relative performance evaluation has come a long way since its inception, so much so that it is now a major research branch in economic theory [...] Full article

(This article belongs to the Special Issue Advances in the Theory and Applications of Contests and Tournaments)

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Special Issue in Games

Learning and Evolution in Games I Guest Editor: Heinrich H. Nax
Deadline: 30 June 2023

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