Essays in game theory

My thesis presents three essays in game theory.; The first chapter provides a detailed analysis of memory in discounted repeated games. A new notion of limited memory, time dependent bounded recall; is proposed, and for any given discounted repeated game, equilibrium outcome paths that satisfy this memory notion is analyzed. We characterize equilibrium outcome paths that can be obtained with time dependent strategies under which the agents do not have to remember more than the outcome that happened in the previous period. It is shown that little is lost.; The second essay is about collusion in moral hazard models. In such models, with two or more agents, the possibility of collusion among agents is often ignored. The essay demonstrates that when two agents can observe and verify each other's effort levels and write binding side contracts, an optimal contract with standard constraints, the incentive compatibility and individual rationality, is not immune to collusion. Formulating the problem and the collusion-proofness constraints, we establish that under standard assumptions there exists an optimal collusion-proof contract. Finally, we characterize optimal wages, and, show that non-decreasing wages are implied by a set of assumptions that involves one that is significantly weaker than the monotone likelihood ratio property.; The third chapter proposes a refinement of Nash equilibria in non-atomic games. In such games, since each agent is atom-less, the possibility of strategic interaction may be completely ignored. To restore strategic interaction among agents, the essay considers a refinement of Nash equilibrium, strategic equilibrium, for non-atomic games where each agent's payoff depends on what he chooses and a societal choice. Given a non-atomic game, we consider a perturbed game in which every player believes that he alone has a small, but positive, impact on the societal choice. A strategy profile is a strategic equilibrium if it is a limit point of a sequence of Nash equilibria of games in which each player's belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, it is shown that every strategic equilibrium must be a Nash equilibrium of the original non-atomic game.