Rational behavior under correlated uncertainty

In complete information games, Dekel and Fudenberg (1990) and Borgers (1994) have proposed the solution concept S∞W (one round of elimination of weakly dominated strategies followed by iterated elimination of strongly dominated strategies), motivating it by a characterization in terms of “approximate common certainty” of admissibility. We examine the validity of this characterization of S∞W in an incomplete information setting. We argue that in Bayesian games with a nontrivial state space, the characterization is very sensitive to the way in which uncertainty in the form of approximate common certainty of admissibility is taken to interact with the uncertainty already captured by players' beliefs about the states of nature: We show that S∞W corresponds to approximate common certainty of admissibility when this is not allowed to coincide with any changes to players' beliefs about states. If approximate common certainty of admissibility is accompanied by vanishingly small perturbations to beliefs, then S∞W is a (generally strict) subset of the predicted behavior, which we characterize in terms of a generalization of Hu's (2007) perfect p-rationalizable set.

[1]  Esslli Site,et al.  Epistemic Game Theory , 2012 .

[2]  J. Mertens,et al.  ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

[3]  H. Keisler,et al.  ADMISSIBILITY IN GAMES , 2008 .

[4]  S. Morris,et al.  The Robustness of Equilibria to Incomplete Information , 1997 .

[5]  D. Fudenberg,et al.  Interim Correlated Rationalizability , 2007 .

[6]  Eddie Dekel,et al.  Hierarchies of Beliefs and Common Knowledge , 1993 .

[7]  Frank Schuhmacher,et al.  Proper rationalizability and backward induction , 1999, Int. J. Game Theory.

[8]  Marciano M. Siniscalchi,et al.  Epistemic Game Theory , 2015 .

[9]  H. Jerome Keisler,et al.  Admissibility in Games1 , 2008 .

[10]  Tilman Börgers,et al.  Weak Dominance and Approximate Common Knowledge , 1994 .

[11]  David M. Kreps,et al.  On the Robustness of Equilibrium Refinements , 1988 .

[12]  Tai-Wei Hu,et al.  On p-rationalizability and approximate common certainty of rationality , 2007, J. Econ. Theory.

[13]  Muhamet Yildiz,et al.  A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements , 2007 .

[14]  T. Tan,et al.  The Bayesian foundations of solution concepts of games , 1988 .

[15]  Pierpaolo Battigalli,et al.  Rationalization and Incomplete Information , 2003 .

[16]  Howard Raiffa,et al.  Games and Decisions: Introduction and Critical Survey. , 1958 .

[17]  David Pearce.  Rationalizable Strategic Behavior and the Problem of Perfection , 1984 .

[18]  D. Fudenberg,et al.  Rational Behavior with Payoff Uncertainty , 1990 .