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# Games, Volume 15, Issue 3 (June 2024) – 4 articles

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8 pages, 247 KiB
Communication
A Controlled Discrete-Time Queueing System as a Model for the Orders of Two Competing Companies
by Mario Lefebvre
Games 2024, 15(3), 19; https://doi.org/10.3390/g15030019 - 29 May 2024
Viewed by 96
Abstract
We consider two companies that are competing for orders. Let ${X}_{1}\left(n\right)$ denote the number of orders processed by the first company at time n, and let $\tau \left(k\right)$ be the first time that [...] Read more.
We consider two companies that are competing for orders. Let ${X}_{1}\left(n\right)$ denote the number of orders processed by the first company at time n, and let $\tau \left(k\right)$ be the first time that ${X}_{1}\left(n\right) or ${X}_{1}\left(n\right)=r$, given that ${X}_{1}\left(0\right)=k$. We assume that $\left\{{X}_{1}\left(n\right),n=0,1,\dots \right\}$ is a controlled discrete-time queueing system. Each company is using some control to increase its share of orders. The aim of the first company is to maximize the expected value of $\tau \left(k\right)$, while its competitor tries to minimize this expected value. The optimal solution is obtained by making use of dynamic programming. Particular problems are solved explicitly. Full article
(This article belongs to the Section Applied Game Theory)
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25 pages, 957 KiB
Article
Information Transmission and Countervailing Biases in Organizations
by Saori Chiba
Games 2024, 15(3), 18; https://doi.org/10.3390/g15030018 - 22 May 2024
Viewed by 317
Abstract
A decision maker (DM) must choose between two projects or decide on no project. The expected benefits of these projects are correlated. The DM seeks advice from an agent with private information about the projects’ benefits. However, the agent’s divergent preferences for projects [...] Read more.
A decision maker (DM) must choose between two projects or decide on no project. The expected benefits of these projects are correlated. The DM seeks advice from an agent with private information about the projects’ benefits. However, the agent’s divergent preferences for projects and lack of consideration for the DM’s implementation costs may introduce two types of biases: project bias, favoring the agent’s project, or pandering bias, favoring the project preferred by the DM. Our findings reveal that project correlation leads to these biases countervailing each other, facilitating the transmission of information. The agent typically recommends a project based on private information to dissuade the DM from choosing no project, as this would be detrimental to the agent. Additionally, we explore optimal delegation within organizations. In contrast to the prevailing literature advocating for delegation to biased agents for enhanced information elicitation, our study suggests limited benefits in the context of project correlation. Full article
14 pages, 299 KiB
Article
Invariant Equilibrium in Discontinuous Bayesian Games
by Blake A. Allison and Jason J. Lepore
Games 2024, 15(3), 17; https://doi.org/10.3390/g15030017 - 20 May 2024
Viewed by 307
Abstract
We provide sufficient conditions on the primitives of a class of discontinuous Bayesian games such that all games in the class share equilibria. If a Bayesian game in the class also satisfies a weak efficiency condition, then we show its normal form is [...] Read more.
We provide sufficient conditions on the primitives of a class of discontinuous Bayesian games such that all games in the class share equilibria. If a Bayesian game in the class also satisfies a weak efficiency condition, then we show its normal form is better-reply secure. The invariance property then provides an existence result for all Bayesian games in the class. Results are shown for both pure strategy and behavioral strategy equilibrium. We illustrate the application of the results with an example of a class of contests with bid caps. Full article
(This article belongs to the Section Non-Cooperative Game Theory)
15 pages, 2987 KiB
Article
Evolution of “Pay-It-Forward” in the Presence of the Temptation to Free-Ride
by Satoshi Uchida, Tatsuya Sasaki, Hitoshi Yamamoto and Isamu Okada
Games 2024, 15(3), 16; https://doi.org/10.3390/g15030016 - 25 Apr 2024
Viewed by 1348
Abstract
“Paying it forward” is a behavior in which people help someone else because they were helped in the past. Although experimental evidence exists that indicates that real human beings often “pay-it-forward” even in the face of free-rider risks, the theoretical basis for the [...] Read more.
“Paying it forward” is a behavior in which people help someone else because they were helped in the past. Although experimental evidence exists that indicates that real human beings often “pay-it-forward” even in the face of free-rider risks, the theoretical basis for the evolution of this behavior remains unclear. In this paper, we propose a game-theoretical model that explains how pay-it-forward behavior can evolve despite the temptation to free-ride. By assuming that human beings exhibit cognitive distortions, as predicted by prospect theory, and that free-riding is punished with a tiny probability, we demonstrate that pay-it-forward, alongside unconditional altruistic behavior, can evolve and effectively deter free-riding behavior. Full article
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