Pure Bayesian Nash Equilibria for Bayesian Games with Multidimensional Vector Types and Linear Payoffs

Sébastien Huot and Abbas Edalat ()
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Sébastien Huot: Department of Computing, Faculty of Engineering, Imperial College London, London SW7 2AZ, UK
Abbas Edalat: Department of Computing, Faculty of Engineering, Imperial College London, London SW7 2AZ, UK

Games, 2025, vol. 16, issue 4, 1-31

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 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).

Keywords: multigame; Bayesian; linear payoff; multidimensional; pure Bayesian Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2025
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