Abstract

Within the theory of games it is typically assumed that players construct hypotheses concerning the contingent play of their opponents based upon the assumption that it is common knowledge that everyone aims at maximizing his payoffs. A necessary condition that a collection of strategies, one for each player, must fulfill in order to be called an equilibrium within a game is that no player might profit from any possible unilateral deviation. This means that players ought to scrutinize the potential consequences of not playing according to the equilibrium. ;The present study starts with the conjecture that the introspective reasoning involved in the decision of how to play a game has a particular epistemological nature in strategic form games with observed actions. The reason is that players might potentially observe and therefore respond to deviations, something which is not possible within simultaneous move games. The premise of the present work is that a proper foundation for the notion of equilibrium in this type of games requires the formalization of strategies as contingent constructions as well as a theory of counterfactuals to analyze the truth condition of the hypothetical reasoning involved in equilibrium. With this purpose the theories of counterfactuals developed by David Lewis and Jonathan Bennett are applied to study different equilibrium notions in particular types of games. ;The first chapter studies the conditions under which the backwards induction solution to the centipede game is compatible with the assumption of common knowledge of maximizing behavior subject to consistent beliefs. The result is that the compatibility between backwards induction and this behavioral assumption is only possible when deviations are assumed to be fully meaningless or unintentional. Otherwise, the corresponding compatibility is assured only in the presence of a lack of knowledge on the part of the players whose extent depends on the length of the game. ;The second chapter studies different equilibrium notions in non simultaneous move games where players are asymmetrically informed. Equilibrium refinements in this type of games crucially depend on how the play of the player who has more information is interpreted. Based upon the theories of counterfactuals presented in the first chapter we study the conditions under which Nash equilibrium exists and how it might be further refined. First a counterexample is provided to show that within the framework under consideration equilibrium need not exist when deviations are considered fully meaningless. Second, a variation of the equilibrium notion called "Divinity" is proposed in order to strength its power to refine the set of sequential equilibria