Self-confirming equilibrium

TL;DR: Self-confirming equilibria as mentioned in this paper are defined as the outcome of a learning process, in which players revise their beliefs using their observations of previous play using a self-confirmant game.

Abstract: rium path of play. Thus, if a self-confirming equilibrium occurs repeatedly, no player ever observes play that contradicts his beliefs, even though beliefs about play at off-path information sets need not be correct. We characterize the ways in which self-confirming equilibria and Nash equilibria can differ, and provide conditions under which self-con- firming equilibria correspond to standard solution concepts. NASH EQUILIBRIUM AND ITS REFINEMENTS describe a situation in which (i) each player's strategy is a best response to his beliefs about the play of his opponents, and (ii) each player's beliefs about the opponents' play are exactly correct. We propose a new equilibrium concept, self-confirming equilibrium, that weakens condition (ii) by requiring only that players' beliefs are correct along the equilibrium path of play. Thus, each player may have incorrect beliefs about how his opponents would play in contingencies that do not arise when play follows the equilibrium, and moreover the beliefs of different players may be wrong in different ways. The concept of self-confirming equilibrium is motivated by the idea that noncooperative equilibria should be interpreted as the outcome of a learning process, in which players revise their beliefs using their observations of previous play. Suppose that each time the game is played, the players observe the actions chosen by their opponents, but that players do not observe the actions their opponents would have played at the information sets that were not reached along the path of play. Then, if a self-confirming equilibrium occurs repeatedly, no player ever observes play that contradicts his beliefs, so the equilibrium is "self-confirming" in the weak sense of not being inconsistent with the evidence. By analogy with the literature on the bandit problem (e.g., Rothschild (1974)) one might expect that a non-Nash self-confirming equilibrium can be the outcome of plausible learning processes. This point was made by Fudenberg and