Regret Equilibria in Games

We study boundedly rational players in an interactive situation. Each player follows a simple choice procedure in which he reacts optimally against a combination of actions of his opponents drawn at random from the distribution generated by a player's beliefs. By imposing a consistency requirement we obtain an equilibrium notion which we call regret equilibrium. An existence proof is provided and it is shown that the concept survives the iterated elimination of never-best responses. Additional properties are studied and the regret equilibrium concept is compared with other game theoretic solution concepts. The regret equilibrium concept is illustrated by means of interesting examples. It is shown that in the centipede game, players will continue to play with large probability.