Bayesian Game Theory: Limitations of Incomplete Information in Determining Probabilities and Payoffs

Abstract

Game theory is a complex area of study based on principles of mathematics and statistics. Simple, two-player games such as the Prisoner’s Dilemma demonstrate the basics of probabilities, outcomes, and payoff matrices. Often, game theory involves games of complete information, where all information is known to all players. Bayesian games explore a specific type of multiplayer game, called games of incomplete information, where some information about the players or the game is unknown. This study analyzes Bayesian games with unknown player identities. The study uses the Prisoner’s Dilemma as a basis for game theory payoff matrices. The Prisoner’s Dilemma is then used as a simple Bayesian game example, followed by a more detailed analysis of the Sheriff’s Dilemma. The study shows that probabilities are much more complex in Bayesian games than in games of complete information. The results demonstrate that the ideal strategy of a player could depend on multiple factors in a Bayesian game. The study concludes that ethical considerations are a significant factor in Bayesian games, and this type of analysis can be applied to a variety of fields. Broader applications include studies in economics, sociology, law, and many other fields.