BELIEFS REVEALED IN BAYESIAN EQUILIBRIUM

Abstract: The prediction of action profiles played in Bayesian Equilibrium (BE) in a game is not well defined over belief hierarchies. Equivalently, by observing the BE action profiles in all games, one can recover more than just standard belief hierarchies. Our main result is to show that extending beliefs to payoff irrelevant facts, signals, brings them to a harmony with BE in the following sense: First, if two type spaces give rise to the same rich hierarchy of beliefs then for every game same action profiles are played in any BE. Secondly, if two type spaces give rise to different rich hierarchies then for some game different action profiles are played in BE.To proove the first part we define the BE explicitly, syntactically, within the rich belief hierarchy. It follows that exactly those action profiles are played in some BE that are consistent with the corresponding richer hierarchy and the common belief of rationality. In other words, our second result is a decision theoretic rationale for BE.

Location: 
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
Dates: 
Sunday, January 21, 2007 - 16:15 to 18:15
Old Lecturers: 
TOMASZ SADZIK
Old Lecturers University: 
STANFORD UNIVERSITY