Perfect Subjective Correlated Equilibrium; Professor Chih-Chun YANG (Institute of Economics, Academia Sinica, Taiwan)

Abstract

We are concerned with the perfect rational behavior in a game where correlation devices are available to players, without the common prior assumption. We propose perfect subjective correlated equilibrium (PSCE) as a perfection of Aumann's (1974) a posteriori equilibrium. Weak proper subjective correlated equilibrium (WPSCE) is defined by imposing "properness" between the nature's trembling hand and players' trembling hands, in alignment with Milgrom and Mollner 's (2021) extended proper equilibrium. We provide full characterization of these two notion of equilibrium. In normal form games, the set of PSCE's in a normal form game is equivalent to Dekel and Fudenberg's (1990) iterative procedure , and every WPSCE coincides with a weak notion of self-admissible set (Brandenburger et al, 2008). In extensive form games, every WPSCE coincides with a notion of "perfect extensive-form rationalizability " We also obtain the counterpart result for the "obvious" equilibrium notions.