Equilibrium Selection in n-Person Static Games with Complete Information

The existence of multiple equilibria in non-cooperative games has long been an issue in game theory. In certain cases, such circumstance is beneficial from an ex-ante perspective, since the evaluation of possible behaviors and plausible outcomes contributes to a deeper understanding of the problem. However, in general, a proper analysis requires the selection of a single solution. The inability of game theory, so far, to recurrently make such prediction not only limits the impact of its respective methods but also raises questions about the general predictive power of the theory itself. This issue has been then the object of two research programs. The most prominent, the refinement program, produced concepts that, although capable of reducing the number of solutions in some games, are commonly unable to lessen the set of equilibria up to a singleton, or even to a subset of reasonable size, and seem to integrate an apparently endless cycle of refinements, instead of a path towards a consensual concept. The alternative, the selection program, has not been more successful, mainly due to the absence of consensus regarding the assumptions, criteria, and methods adequate to select a solution. In this context, it is proposed an equilibrium selection method to n-person static games with complete information and a finite set of equilibria, where criteria of risk and payoff dominance are defined and used to order players’ preferences over the solutions of a reduced version of the game. It is shown that in this class of games a unique equilibrium either in pure or mixed action- s or a unique correlated equilibrium is selected, the last characterized by the fact that players correlate their actions based on an endogenous and commonly known feature of the game, which consequently allows this solution to be self-enforcing without pre-play communication.