Jernej Čopič: Nash equilibrium, rational expectations, and heterogeneous beliefs
Source: Seminar for probability, statistics, and financial mathematics
In this presentation I will focus mostly on action-consistent Nash equilibrium. This first part of the presentation will follow closely the paper co-authored with Andrea Galeotti.
In an action-consistent Nash equilibrium of a simultaneous-moves game with uncertainty a la Harsanyi (1967) players choose optimally, make correct assessments regarding others' actions, and infer information from others' optimal play.
In equilibrium, players may have differing information in the sense of prior beliefs. An example of action-consistent Nash equilibrium strategy profile is constructed, which is not a Nash equilibrium under any common prior. Given the equilibrium strategy profile, each type of each player faces pooling of the other players' types. In a modified example one type of one player doesn't face such a pooling problem: the strategy profile can still satisfy equilibrium conditions up to an arbitrary finite order, but no longer in an infinite regress of action-consistent Nash equilibrium.
Time permitting, I will then give a more applied motivation for as to why such theoretical constructs might be of practical relevance. Finally, I will outline the more general case when the underlying consistency criterion, in the sense of correctness of assessments need not be given by others' actions and own payoffs but by some more general information partition.