This volume collects almost two decades of joint work of Sergiu Hart and Andreu Mas-Colell on game dynamics and equilibria. The starting point was the introduction of the adaptive strategy called <i>regret-matching</i>, which on the one hand is simple and natural, and on the other is shown to lead to...

AbstractWe exhibit a large class of simple rules of behavior, which we call adaptive heuristics, and show that they generate rational behavior in the long run. These adaptive heuristics are based on natural regret measures, and may be viewed as a bridge between rational and behavioral...

AbstractHart and Mas-Colell (2000) show that if all players play “regret matching” strategies, i.e., they play with probabilities proportional to the regrets, then the empirical distribution of play converges to the set of correlated equilibria, and the regrets of every player converge to...

AbstractWe study the question of how long it takes players to reach a Nash equilibrium in uncoupled setups, where each player initially knows only his own payoff function. We derive lower bounds on the communication complexity of reaching a Nash equilibrium, i.e., on the number of bits that need...

AbstractJohn F. Nash, Jr., submitted his Ph. D. dissertation entitled Non-Cooperative Games to Princeton University in 1950. Read it 58 years later, and you will find the germs of various later developments in game theory. Some of these are presented below, followed by a discussion of dynamic...

AbstractAn elementary proof, based on linear duality, is provided for the existence of correlated equilibria in finite games. The existence result is then extended to infinite games, including some that possess no Nash equilibria.

AbstractWe study the problem of reaching a pure Nash equilibrium in multi-person games that are repeatedly played under the assumption of uncoupledness: every player knows only his own payoff function. We consider strategies that can be implemented by finite-state automata, and characterize the...