Crime and punishment: Further reflections on the counter­intuitive results of mixed equilibria games

In a series of related articles, George Tsebelis (1989, 1990, 1991) challenges political theorists to rethink the foundations of policy analysis. His major critique of policy analyses, based on decision theory (where one individual decides in an inanimate but not certain environment) rather than on game theory (where one individual decides in an environment with other strategic individuals), has weathered the storm of commentaries made on his work. Tsebelis's argument, that payoff changes for one player do not affect the behavior of that player at a mixed-strategy equilibrium, holds in some cases but not in others. Whether changes in the payoffs of one player affect that player's behavior at a mixed-strategy equilibrium depends upon the type of linkages that exist between that player and the others in the frame or in a similar position in a game. In this note we have stated the general conditions under which changes in the payoffs of one player do not affect that player's behavior at equilibrium and when they do.