We propose a simple adaptive procedure for playing strategic games: average testing. In this procedure each player sticks to her current strategy if it yields a payoff that exceeds her average payoff by at least some fixed ε0; otherwise she chooses a strategy at random. We consider generic...

We consider uncoupled dynamics (i.e., dynamics where each player knows only his own payoff function) that reach Pareto efficient and individually rational outcomes. We prove that the number of periods it takes is in the worst case exponential in the number of players.

We study the problem of reaching Nash equilibria 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 minimal number...

A completely uncoupled dynamic is a repeated play of a game, where each period every player knows only his action set and the history of his own past actions and payoffs. One main result is that there exist no completely uncoupled dynamics with finite memory that lead to pure Nash equilibria...

We consider small-influence anonymous games with a large number of players $n$ where every player has two actions. For this class of games we present a best-reply dynamic with the following two properties. First, the dynamic reaches Nash approximate equilibria fast (in at most $cn\ log n$ steps...

R. J. Aumann and J. H. Drèze (2008) define a rational expectation of a player i in a game G as the expected payo of some type of i in some belief system for G in which common knowledge of rationality and common priors obtain. Our goal is to characterize the set of rational expectations in terms...

In 1995, Aumann showed that in games of perfect information, common knowledge of rationality is consistent and entails the back- ward induction (BI) outcome. That work has been criticized because it uses "counterfactual" reasoning|what a player "would" do if he reached a node that he knows he...

The logic of backward induction (BI) in perfect information (PI) games has been intensely scrutinized for the past quarter century. A major development came in 2002, when P. Battigalli and M. Sinischalchi (BS) showed that an outcome of a PI game is consistent with common strong belief of utility...

Infinite sequential games, in which Nature chooses a Borel winning set and reveals it to one of the players, do not necessarily have a value if Nature has 3 or more choices. The value does exist if Nature has 2 choices. The value also does not necessarily exist if Nature chooses from 2 Borel...