Essays on economic theory

These four essays concern the theory of games and its application to economic theory. The first two, closely linked, chapters are an investigation into the foundational question of the sensitivity of the predictions of game theory to higher-order beliefs. Impact of Higher-Order Uncertainty with Muhamet Yildiz In some games, the impact of higher-order uncertainty is very large, implying that present economic theories may be misleading as these theories assume common knowledge of the type structure after specifying the first or the second orders of beliefs. Focusing on normal-form games in which the players' strategy spaces are compact metric spaces, we show that our key condition, called "global stability under uncertainty," implies a variety of results to the effect that the impact of higher-order uncertainty is small. Our central result states that, under global stability, the maximum change in equilibrium strategies 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 strategies by specifying only finitely many orders of beliefs. Finite-Order Implications of Any Equilibrium with Muhamet Yildiz Present economic theories make a common-knowledge assumption that implies that the first or second-order beliefs determine all higher-order beliefs.