Buridan's ass in coordination games



Consider a simple coordination game. In this game, two players (player 1 and player 2) each simultaneously choose an action, X or Y. If they both choose X, they both get 1 utility. If they both choose Y, they both get utility for some known to both players. If they choose different actions, they both get 0 utility. Which action should they each choose? Assume they get to communicate before knowing , but not after knowing .

An optimal policy pair is for each to pick X if , and Y otherwise. Unfortunately, this policy pair can break down in the presence of even a small amount of noise. Assume neither player observes , but instead each receives an independent observation (player 1 sees , player 2 sees