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
Asymmetric Reimbursement and Contingent Fees in Environmental Conflicts: Observable vs. Unobservable Contracts
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
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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.
Full article
(This article belongs to the Special Issue Game Theory with Applications to Economics)
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Open AccessArticle
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.
Full article
(This article belongs to the Special Issue Advances in Game Theory, Multi-Agent Systems, and Computer Security)
Open AccessArticle
Some Properties of Interval Shapley Values: An Axiomatic Analysis
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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.
Full article
(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.
Full article
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.
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
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.
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
Games 2023, 14(3), 44; https://doi.org/10.3390/g14030044 - 26 May 2023
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
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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 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
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
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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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Invasion of Optimal Social Contracts
Games 2023, 14(3), 42; https://doi.org/10.3390/g14030042 - 15 May 2023
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
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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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Social Learning for Sequential Driving Dilemmas
Games 2023, 14(3), 41; https://doi.org/10.3390/g14030041 - 11 May 2023
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
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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.
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(This article belongs to the Special Issue Learning and Evolution in Games I)
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First You Get the Money, Then You Get the Power: The Effect of Cheating on Altruism
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Games 2023, 14(3), 40; https://doi.org/10.3390/g14030040 - 04 May 2023
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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
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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.
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On Some Connections between Negotiating while Fighting and Bargaining between a Buyer and Seller
Games 2023, 14(3), 39; https://doi.org/10.3390/g14030039 - 28 Apr 2023
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
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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
Games 2023, 14(3), 38; https://doi.org/10.3390/g14030038 - 28 Apr 2023
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
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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
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Games 2023, 14(3), 37; https://doi.org/10.3390/g14030037 - 28 Apr 2023
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
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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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Improving Strategic Decisions in Sequential Games by Exploiting Positional Similarity
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Games 2023, 14(3), 36; https://doi.org/10.3390/g14030036 - 28 Apr 2023
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
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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.
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(This article belongs to the Special Issue Negotiations: The Good, the Bad, and the Ugly)
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Special Issues
Special Issue in
Games
Game Theory for Cybersecurity and Privacy
Guest Editors: Mohammad Mahdi Khalili, Xueru ZhangDeadline: 31 August 2023
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