Suppose that each player in a game is rational, each player thinks the other players are rational, and so on. Also, suppose that rationality is taken to incorporate an admissibility requirement — that is, the avoidance of weakly dominated strategies. Which strategies can be played? We provide...

Game-theoretic analysis often leads to consideration of an infinite hierarchy of beliefs for each player. Harsanyi suggested that such a hierarchy of beliefs could be summarized in a single entity, called the player's type. This chapter provides an elementary construction, complementary to the...

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...

Best-response sets (Pearce [1984]) characterize the epistemic condition of “rationality and common belief of rationality.” When rationality incorporates a weak-dominance (admissibility) requirement, the self-admissible set (SAS) concept (Brandenburger, Friedenberg, and Keisler [2008])...

Two properties of preferences and representations for choice under uncertainty which play an important role in decision theory are: (i) admissibility, the requirement that weakly dominated actions should not be chosen; and (ii) the existence of well defined conditional probabilities, that is,...

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.

We discuss the unity between the two standard approaches to noncooperative solution concepts for games. The decision-theoretic approach starts from the assumption that the rationality of the players is common knowledge. This leads to the notion of correlated rationalizability. It is shown that...

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...

Correlations arise naturally in noncooperative games, e.g., in the equivalence between undominated and optimal strategies in games with more than two players. But the noncooperative assumption is that players do not coordinate their strategy choices, so where do these correlations come from? The...