Game-Theoretical Approaches to Power

Game theory analyzes social situations of interdependent decision making, wherein the outcome depends on the choices of two or more decision makers or players. By comparison, decision theory focuses on one-person games, or games against nature, wherein the outcome depends of the choice of one player and “nature,” which is assumed not to have preferences and whose actions instead occur with specified probabilities.

With the exception of the power indices, some of which are rooted in cooperative game theory, power is not much studied in game theory. In noncooperative game theory, which does not assume a contract is binding, players are usually assumed to have an equal ability to influence the outcome.

To be sure, players may play different roles (e.g., attacker vs. defender) and so have different preferences. But how stable outcomes, or equilibria in games, depend on the abilities of players to exert influence is rarely analyzed.

In the absence of a theory that considers power differences among players in noncooperative games, this entry begins with three examples in which power matters—exercising it may change the outcome. But, paradoxically, it may not change the outcome in favor of the player that possesses it. Actually, the examples demonstrate that the player with ostensibly the most power may be hurt by possessing it.

Next, the entry describes a well-known sequential game in which a powerful player can induce less powerful players not to compete with it, but [Page 271]this game, too, has a paradoxical aspect. Finally, the entry briefly discusses how order, moving, and threat power in Steven J. Brams's theory of moves may enable players to achieve preferred outcomes.

What game theory adds to the analysis of power is how its exercise is conditioned by the strategic interaction of the players. Thus, the first example illustrates how a game in which a chair and other voters are embedded induces the other voters to “gang up” against the chair, undermining its seemingly greater power. A similar problem arises for the best shooter in the second example, and the omniscient player in the third example when its opponent knows it is omniscient.

But the greater ability of a player to control the outcome—a standard measure of power—does help players achieve their goals in most games. Game theory clarifies when this is the case, and it elucidates subtleties in the exercise of power that would not be apparent without it.