Nash Equilibria of Games When Players' Preferences Are Quasi-Transitive

Much of game theory is founded on the assumption that individual players are endowed with preferences that can be represented by a real-valued utility function. However, in reality human preferences are often not transitive. This is especially true for the indifference relation, which can lead an individual to make a series of choices which in their totality would be viewed as erroneous by the same individual. There is a substantial literature that raises intricate questions about individual liberty and the role of government intervention in such contexts. The aim of this paper is not to go into these ethical matters but to provide a formal structure for such analysis by characterizing games where individual preferences are quasi-transitive. The paper identifies a set of axioms which are sufficient for the existence of Nash equilibria in such 'games.'