Impossibility theorems for normal form games

Abstract

Two recent papers (Cubitt and Sugden, 1994; Samuelson, 1992) have established impossibility results which cast doubt on the coherence of the assumption of ’common knowledge of rationality'. It is shown that the Cubitt–Sugden result is the more powerful of the two impossibilities. Second, it is proved that the existence of a quasi-strict equilibrium is sufficient to construct sets which satisfy the Cubitt–Sugden axioms. This fact is used to establish that their impossibility result cannot arise in 2-player games. Finally, it is shown that if a weak symmetry postulate is added, a new impossibility result arises for this class of games.