Uncertainty Aversion and Equilibrium

If rationality is not mutual knowledge in a game then standard expected utility theory requires a rational player to have a specific belief about the behaviour of a non-rational opponent. This paper argues that this problem does not arise under Choquet expected utility theory, which does not require a player's beliefs to be additive. Non-additive beliefs allow the formalization of the idea that a player who faces a non-rational opponent faces genuine uncertainty. Optimal strategies can then be derived from assumptions about the rational player's attitude towards uncertainty. This paper investigates the consequences of such a view of strategic interaction. We formulate equilibrium concepts, called Choquet–Nash equilibrium in normal forms and perfect Choquet equilibrium in extensive forms, that solves the infinite regress that arises in this situation and study existence and properties of these equilibria in normal and extensive form games.