Equivalence and Stooge Strategies in Zero-Sum Games

Abstract

Classes of two-person zero-sum games termed "equivalent games" are defined. These are games with identical value and identical optimal mixed-strategies but with different matrix entries and thus different opportunities for exploiting a nonrational opponent. An experiment was conducted to investigate the strategy-choice behavior of subjects playing pairs of these "equivalent games." Also investigated was the extent to which subjects would exploit a programmed stooge as a function of the degree to which the stooge departed from his optimal strategy mix. The results indicated that subjects learned to exploit the nonrational play of the stooge opponent. The game factor, on the other hand, seemed to have no significant effect upon the strategy-choice behavior of the players. The implications of these results are discussed in light of questions raised by previous research on decision-making in 2 x 2 zero-sum games.