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.

In this thesis we study decentralized dynamics for non-cooperative and cooperative games. The dynamics are behaviorally motivated and assume that very little information is available about other players' preferences, actions, or payoffs. For example, this is the case in markets where exchanges are frequent and the sheer size of the market hinders participants from learning about others' preferences. We consider learning dynamics that are based on trial-and-error and aspiration-based heuristics. Players occasionally try to increase their performance given their current payoffs. If successful they stick to the new action, otherwise they revert to their old action. We also study a dynamic model of social influence based on findings in sociology and psychology that people have a propensity to conform to others' behavior irrespective of the payoff consequences. We analyze the dynamics with a particular focus on two questions: How long does it take to reach equilibrium and what are the stability and welfare properties of the equilibria that the process selects? These questions are at the core of understanding which equilibrium concepts are robust in environments where players have little information about the game and the high rationality assumptions of standard game theory are not very realistic. Methodologically, this thesis builds on game theoretic techniques and prominent solution concepts such as the Nash equilibrium for non-cooperative games and the core for cooperative games