Noncooperative games and nontransitive preferences

A proof exactly analogous to Nash's proof for the existence of equilibria in finite noncooperative games with von Neumann-Morgenstern utilities shows that such games have Nash equilibria when preferences satisfy the weaker conditions of ‘SSB utility theory’. An example illustrates the dual roles of mixed strategies in the SSB game context, namely to disguise a player's actual strategy choice and to resolve the potential intrapersonal dilemma of cyclic preferences among pure strategies.