Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating "never-best-reply" strategies does not terminate after the...

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...

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...

Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating "never-best-reply" strategies terminates before or at the...

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 \epsilon 0; otherwise she chooses a strategy at random. We consider...

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...

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...