A Game with No Bayesian Approximate Equilibria

Authors: 
Ziv Hellman
Abstract: 

Simon (2003) presented an example of a 3-player Bayesian games with no Bayesian equilibria but it has been an open question whether or not there are games with no approximate Bayesian equilibria. We present an example of a Bayesian game with two players, two actions and a continuum of states that possesses no approximate Bayesian equilibria, thus resolving the question. As a side benefit we also have for the first time an an example of a 2-player Bayesian game with no Bayesian equilibria and an example of a strategic-form game with no approximate Nash equilibria. The construction makes use of techniques developed in an example by Y. Levy of a discounted stochastic game with no stationary equilibria.

Date: 
July, 2012
Number: 
615