On Stalnaker's Notion of Strong Rationalizability and Nash Equilibrium in Perfect Information Games

Theory and Decision 45 (3):291-295 (1998)

Authors
Giacomo Bonanno
University of California, Davis
Abstract
Counterexamples to two results by Stalnaker (Theory and Decision, 1994) are given and a corrected version of one of the two results is proved. Stalnaker's proposed results are: (1) if at the true state of an epistemic model of a perfect information game there is common belief in the rationality of every player and common belief that no player has false beliefs (he calls this joint condition ‘strong rationalizability’), then the true (or actual) strategy profile is path equivalent to a Nash equilibrium; (2) in a normal-form game a strategy profile is strongly rationalizable if and only if it belongs to C8 , the set of profiles that survive the iterative deletion of inferior profiles
Keywords Nash equilibrium  Perfect information games  Stalnaker's notion
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DOI 10.1023/A:1005090905103
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