Impact of higher-order uncertainty

In some games, the impact of higher-order uncertainty is very large, implying that present economic theories may rely critically on the strong common knowledge assumptions they make. Focusing on normal-form games in which the players' action spaces are compact metric spaces, we show that our key condition, called "global stability under uncertainty," implies that the maximum change in equilibrium actions due to changes in players' beliefs at orders higher than k is exponentially decreasing in k. Therefore, given any need for precision, we can approximate equilibrium actions by specifying only finitely many orders of beliefs.