The Context of the Game

Joint with: Martin Meier

Here, we study games of incomplete information, and argue that it is important to correctly specify the “context” within which hierarchies of beliefs lie. We consider a situation where the players understand more than the analyst, in the following sense: It is transparent to the

players–but not to the analyst–that certain hierarchies of beliefs are precluded. In particular, the players’ type structure can be viewed as a strict subset of the analyst’s type structure. How does this affect a Bayesian equilibrium analysis? One natural conjecture is that this doesn’t

change the analysis–i.e., every equilibrium of the players’ type structure can be associated with an equilibrium of the analyst’s type structure. We show two reasons why this conjecture is wrong. So, Bayesian Equilibrium fails, what we call, the Extension Property. We go on to discuss specific situations in which the Extension Property is satisfied. This involves restrictions on the game and the type structures.

For more information, contact Jing Li.