Information-Invariant Equilibria of Extensive Games

Abstract

The paper studies the concept of ``ex post equilibrium" that has recently become popular in literature on auctions, mechanism design and implementation. We ask how one should define ex post equilibrium if one wants to consider extensive games, such as dynamic auctions, and if one wants to include sequential rationality in the equilibrium definition. As it turns out, this raises some conceptual questions that are not present in the static setting. We are lead to introduce three different definitions - all variations of what we call ``information-invariant equilibrium." One of these three definitions is equivalent to ``ex post equilibrium." In static games the three definitions coincide. In extensive games they do not - if we impose sequential rationality. Our main purpose is to make a methodological contribution to game theory, but we illustrate the relevance of this contribution by applying our concepts to several auction games.