Games

10 pages, 292 KiB

Open AccessArticle

Some Properties of Interval Shapley Values: An Axiomatic Analysis

by Shinichi Ishihara and Junnosuke Shino

Games 2023, 14(3), 50; https://doi.org/10.3390/g14030050 - 15 Jun 2023

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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 [...] Read more.

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. Full article

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

16 pages, 337 KiB

Open AccessArticle

Gender and Risk Aversion: Evidence from a Natural Experiment

by Luís Pacheco, Júlio Lobão and Sílvia Coelho

Games 2023, 14(3), 49; https://doi.org/10.3390/g14030049 - 14 Jun 2023

Viewed by 1657

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 [...] Read more.

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. Full article

22 pages, 1388 KiB

Open AccessArticle

Optimal Contest Design When Policing Damaging Behavior

by Scott M. Gilpatric and Ye Hong

Games 2023, 14(3), 48; https://doi.org/10.3390/g14030048 - 13 Jun 2023

Viewed by 973

Abstract

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 [...] Read more.

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. Full article

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14 pages, 314 KiB

Open AccessArticle

Simple Mediation in a Cheap-Talk Game

by Chirantan Ganguly and Indrajit Ray

Games 2023, 14(3), 47; https://doi.org/10.3390/g14030047 - 02 Jun 2023

Viewed by 1116

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 [...] Read more.

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. Full article

31 pages, 1917 KiB

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

Viewed by 1469

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 [...] 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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16 pages, 1797 KiB

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

Viewed by 1428

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 [...] 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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8 pages, 278 KiB

Open AccessArticle

Training, Abilities and the Structure of Teams

by Tobias Hiller

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

Cited by 1 | Viewed by 1105

Abstract

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)

24 pages, 487 KiB

Open AccessArticle

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

by Zhongwen Chen and Xiaojian Zhao

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

Cited by 1 | Viewed by 1192

Abstract

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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14 pages, 994 KiB

Open AccessArticle

Invasion of Optimal Social Contracts

by Alessandra F. Lütz, Marco Antonio Amaral, Ian Braga and Lucas Wardil

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

Cited by 1 | Viewed by 1183

Abstract

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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12 pages, 637 KiB

Open AccessArticle

Social Learning for Sequential Driving Dilemmas

by Xu Chen, Xuan Di and Zechu Li

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

Viewed by 1303

Abstract

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, 1st Edition)

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21 pages, 564 KiB

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

Cited by 1 | Viewed by 1837

Abstract

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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9 pages, 230 KiB

Open AccessArticle

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

by Adam Meirowitz

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

Viewed by 1088

Abstract

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)

21 pages, 332 KiB

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

Viewed by 1497

Abstract

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)

19 pages, 545 KiB

Open AccessArticle

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

by Charlotte Roman and Paolo Turrini

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

Viewed by 1237

Abstract

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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13 pages, 493 KiB

Open AccessArticle

Improving Strategic Decisions in Sequential Games by Exploiting Positional Similarity

by Sabrina Evans and Paolo Turrini

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

Viewed by 1361

Abstract

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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20 pages, 390 KiB

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

Viewed by 1282

Abstract

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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9 pages, 333 KiB

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

Viewed by 3620

Abstract

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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Games, Volume 14, Issue 3 (June 2023) – 17 articles

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