An individual facing a problem of choice under uncertainty behaves optimally given beliefs about the relevant unknown factors. When these include other agents' choices, some beliefs are more reasonable than others. The standard equilibrium notions in game theory require that, at a minimum, a player's beliefs agree with other players' prescribed behavior. In equilibrium, then, individual behavior is both optimal and coordinated. Repeated interaction enables coordination based on observation of past moves. In one-shot situations, coordination arises from exchange of information before actual choices are made. The first chapter of this dissertation is concerned with the question of whether coordination in infinitely repeated games is affected by the natural assumption that observation of past moves is imperfect and players choose not to recall far past events. We show that in many cases this assumption has the strong consequence of completely undoing the possibility of coordination. In the second chapter, we consider one-shot situations where players can exchange information through an external mediator before choosing, under the assumption that communication is restricted in that the mediator can only make public recommendations. The result is that the possibility of coordination is completely insensitive to this restriction, provided rich sets of messages are available. In both of the first chapters it is assumed that each player attaches a utility number to every outcome and then ranks strategies by the mathematical expectations of their utility. It is further assumed informally that each player believes other players similarly assess the desirability of their strategies. The third chapter deals with the foundational problem of what these assumptions mean in terms of the individual's personal attitude towards uncertain prospects. The main results--appropriate extensions of classical results in one-agent theory--establish rules on subjective preference which fully characterize the assumption that each player is an expected utility maximizer, believes every other player is, believes every other player believes every other player is, and so on.
