## EQUILIBRIUM DEPARTURES FROM COMMON KNOWLEDGE IN GAMES WITH NON-ADDITIVE EXPECTED UTILITY

## Sujoy Mukerji

### Dept of Economics, University of Southampton

### and

### Nuffield College, Oxford University

### September 1997

Abstract

In a game where the players have non-additive beliefs, we explore the beliefs implicit in the equilibrium behaviour of the players. Under one interpretation, we can show that there are well-defined departures from common knowledge of the game among the players. Our argument revolves around a representation theorem which relates equilibrium under non-additive beliefs to equilibrium actions of a set of types in a Bayesian game with a common prior. Among these types, the game is common *p*-belief, where the p depends on the degree of uncertainty aversion. Only when the beliefs are additive is *p=1*.