It can be smart to be stupid

David Wolpert, NASA Ames Research Center

Abstract: An important problem in game theory is how to explain bounded rationality in general, and altruism to non-kin in particular. Previous explanations have involved computational limitations on the players, repeated plays of the same game among the players, signaling among the players, networks of which players play with one another, etc. As an alternative I show how a simple modification to any game can make bounded rationality be optimal for that game. In particular, this modification can make altruism to non-kin be optimal.

Intuitively, the idea of this extension is that before playing the game, the players all adopt ``personas" that determine how they will act in the game. By changing her choice of persona, a player will induce the other players to make different choices in the game. In particular, sometimes by adopting a bounded rational persona, a player i will induce the other players to change their choices in a way that benefits i. When that is the case, player i's adopting that ``bounded rational'' persona is actually optimal for i.

As particular illustrations, I show how such persona games can explain some experimental observations concerning the prisoner's dilemma, the ultimatum game, and the traveler's dilemma game. I also discuss the possible implications of persona games for evolutionary biology, for the concept of social intelligence, and for distributed control of systems of systems.