zbMATH — the first resource for mathematics

Common belief and the theory of games with perfect information. (English) Zbl 0802.90126
Summary: The statement “it is common belief that player \(i\) is Bayesian rational” (where Bayesian rational means an expected utility maximizer) is defined for two-person games with perfect information. It is shown that in most such games it is not possible for a theory to postulate the Bayesian rationality of all players and to be common belief. This bears directly upon the salience of standard solution concepts such as subgame perfect, and sequential equilibria as well as upon the extensive form rationalizability theories of D. Bernheim [Econometrica 52, 1007- 1028 (1984; Zbl 0552.90098)] and D. Pearce [Econometrica 52, 1029- 1050 (1984; Zbl 0552.90097)] which rely heavily on the common belief of Bayesian rationality.

91A05 2-person games
Full Text: DOI