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Volume 16
Issue 4
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Games, Volume 16, Issue 4 (August 2025) – 6 articles

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31 pages, 883 KiB  
Article
Pure Bayesian Nash Equilibria for Bayesian Games with Multidimensional Vector Types and Linear Payoffs
by Sébastien Huot and Abbas Edalat
Games 2025, 16(4), 37; https://doi.org/10.3390/g16040037 (registering DOI) - 14 Jul 2025
Abstract
In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a [...] Read more.
In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a discrete type space and those with a continuous type space. More specifically, we are interested in the existence of pure Bayesian Nash equilibriums for such games and efficient algorithms to find them. For continuous priors, we suggest a methodology to perform Nash equilibrium searches in simple cases. For discrete priors, we present algorithms that can handle two-action and two-player games efficiently. We introduce the core concept of threshold strategy and, under some mild conditions, we show that these games have at least one pure Bayesian Nash equilibrium. We illustrate our results with several examples like the double-game prisoner’s dilemma (DGPD), the game of chicken, and the sustainable adoption decision problem (SADP). Full article
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33 pages, 3140 KiB  
Article
“Anything Goes” in an Ultimatum Game?
by Peter Paul Vanderschraaf
Games 2025, 16(4), 36; https://doi.org/10.3390/g16040036 - 9 Jul 2025
Viewed by 291
Abstract
I consider an underexplored possible explainer of the “surprising” results of Ultimatum Game experiments, namely, that Proposers and Recipients consider following only some of all the logically possible strategies of their Ultimatum Game. I present an evolutionary analysis of different games having the [...] Read more.
I consider an underexplored possible explainer of the “surprising” results of Ultimatum Game experiments, namely, that Proposers and Recipients consider following only some of all the logically possible strategies of their Ultimatum Game. I present an evolutionary analysis of different games having the same set of allowable Proposer offers and functions that determine Proposer and Recipient payoffs. For Unrestricted Ultimatum Games, where Recipients may choose from among any of the logically possible pure strategies, populations tend to evolve most often to Nash equilibria where Proposers make the lowest allowable offer. However, for Threshold Reduced Ultimatum Games, where Recipients must choose from among minimum acceptable offer strategies, and for Range Reduced Ultimatum Games, where Recipients must choose from among pure strategies that spurn offers that are “too high” as well as “too low”, populations tend to evolve most often to Nash equilibria where Proposers offer substantially more than the lowest possible offer, a result that is consistent with existing Ultimatum Game experimental results. Finally, I argue that, practically speaking, actual Proposers and Recipients will likely regard some reduction of the Unrestricted Ultimatum Game as their game because, for them, the strategies of this reduction are salient. Full article
(This article belongs to the Special Issue Evolution of Cooperation and Evolutionary Game Theory)
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17 pages, 329 KiB  
Article
Pool Formation with Three Patent Owners
by Hao Liu, Xuewen Qian, Chen Qu and Jingyi Shen
Games 2025, 16(4), 35; https://doi.org/10.3390/g16040035 - 8 Jul 2025
Viewed by 169
Abstract
We analyze the endogenous formation of patent pools among three patent owners and the associated welfare effects. Under a condition of synergistic three-patent combination, either a unique symmetric equilibrium or infinitely many asymmetric equilibria can arise when patents are fragmented. By using the [...] Read more.
We analyze the endogenous formation of patent pools among three patent owners and the associated welfare effects. Under a condition of synergistic three-patent combination, either a unique symmetric equilibrium or infinitely many asymmetric equilibria can arise when patents are fragmented. By using the notion of equilibrium binding agreements, we show that (1) when there is a unique symmetric equilibrium under fragmented patents, the complete pool is both stable and welfare-maximizing; (2) fragmented patents are stable in the presence of infinitely many asymmetric equilibria; and (3) when considering only a single specific asymmetric equilibrium under fragmented patents, the complete pool is welfare-maximizing if it is stable, while fragmented patents can be both stable and welfare-maximizing under certain conditions. We also discuss an alternative version of synergism and an alternative bargaining protocol for patent pool formation. Full article
(This article belongs to the Section Cooperative Game Theory and Bargaining)
24 pages, 468 KiB  
Article
Hierarchies and Promotions in Political Institutions: Accountability and Selection
by B. Pablo Montagnes, Stephane Wolton and Junyan Jiang
Games 2025, 16(4), 34; https://doi.org/10.3390/g16040034 - 4 Jul 2025
Viewed by 248
Abstract
Hierarchies are common in political settings. From judges to elected politicians, as well as from activists to bureaucrats, political agents compete for promotion to higher positions. This paper studies political tournaments and their impact on two aspects of political performance: accountability and selection. [...] Read more.
Hierarchies are common in political settings. From judges to elected politicians, as well as from activists to bureaucrats, political agents compete for promotion to higher positions. This paper studies political tournaments and their impact on two aspects of political performance: accountability and selection. While larger tournaments discourage effort, they improve selection. We also discuss the optimal design of tournaments as a function of the principal’s objectives and the features of the environment. We find that tournaments of size two (such as two-candidate elections) are generally suboptimal. Our analysis also highlights that increased desirability of promotion always increases effort but can reduce the optimal tournament size under certain conditions. We also present a range of other comparative statics. Full article
(This article belongs to the Special Issue Conflict and Communication: Applications of Game Theory to Political Economy)
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13 pages, 596 KiB  
Article
Nonmarket Valuation by Contests Under Two American Rules: A Game-Theoretic Analysis
by Sung-Hoon Park and Jason F. Shogren
Games 2025, 16(4), 33; https://doi.org/10.3390/g16040033 - 30 Jun 2025
Viewed by 346
Abstract
Herein, we further examine how we can value nonmarket goods and services by considering the costs associated with environmental conflicts. Focusing on two American rules—the asymmetric reimbursement system and the contingent fee contract—we develop a strategic game-theoretic model in which a citizens group [...] Read more.
Herein, we further examine how we can value nonmarket goods and services by considering the costs associated with environmental conflicts. Focusing on two American rules—the asymmetric reimbursement system and the contingent fee contract—we develop a strategic game-theoretic model in which a citizens group engages a delegate through a contingent fee compensation contract, while a polluter engages a delegate through an hourly fee compensation contract. If the citizens group prevails, the polluter is obligated to contribute a portion of the contingent fee. Solving for the subgame perfect equilibrium, two results emerge. First, the 4x-rule can be maintained through the adjustment of the asymmetric reimbursement system. Second, the asymmetric reimbursement system can serve both as a supplementary method to measure nonmarket valuation and to reduce the rent dissipation resulting from environmental conflicts under general circumstances. Full article
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16 pages, 336 KiB  
Article
The Impact of Market Mood on a Dynamic Model of Insider Trading
by Ruohan Wang, Jing Wang and Zhi Yang
Games 2025, 16(4), 32; https://doi.org/10.3390/g16040032 - 20 Jun 2025
Viewed by 354
Abstract
According to the research, the proportions of various types of investors may or may not change in response to different trading strategies or complex trading environments. This paper investigates a single-period trading model for multiple risk-averse and risk-neutral insider traders. The distinction is [...] Read more.
According to the research, the proportions of various types of investors may or may not change in response to different trading strategies or complex trading environments. This paper investigates a single-period trading model for multiple risk-averse and risk-neutral insider traders. The distinction is that we consider the impact of the number of risk-averse traders and different types of insider traders on market liquidity. The model contains four types of trading entities: risk-neutral and risk-adverse insider traders, risk-neutral market makers, and noise traders. Firstly, we prove the existence and uniqueness of the model’s linear Nash equilibrium; secondly, we compare the model with multiple risk-neutral and risk-adverse insider traders in the market to the model with only risk-neutral insider traders and risk-adverse insider traders. It is shown that the market liquidity parameter λ decreases with the increase in the number of risk-averse persons N2 in a particular range and increases with the increase in the number of risk-averse persons N2 in another range. Markets with risk-neutral and risk-averse insider traders have consistently lower liquidity than markets with only risk-neutral insider traders. Comparing this to markets with only risk-adverse insider traders reveals that the number of risk-adverse traders heavily influences market liquidity. Full article
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