GAMES WITH REPEATED DECISIONS

Extensive form games are traditionally required to obey the axiom of 'nonrepetition': No information set may contain more than one node from any directed path in the tree. However, in order to model games where the players are teams or automata, it is necessary to consider extensive forms which do not satisfy the nonrepetition axiom. This paper develops a noncooperative strategic theory for such games. Mixed or behavioral strategies are inadequate for such games, but there always exist Nash equilibria in finite combinations of behavioral strategies. It can also be shown that any given pair of such strategies form the unique Nash equilibrium for some two person zero-sum game.