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2015 | OriginalPaper | Chapter

7. Perfect Bayesian Equilibrium

Author : Takako Fujiwara-Greve

Published in: Non-Cooperative Game Theory

Publisher: Springer Japan

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Abstract

In this chapter we consider extensive-form games in which the payoff functions are not common knowledge. We introduce the concept of Perfect Bayesian Equilibrium and analyze signaling games.

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previous chapter Bayesian Nash Equilibrium

next chapter Equilibrium Refinements

Alternatively, the sender can maximize the ex-ante expected payoff, as with a Baysian Nash equilibrium.

There are also behavioral strategies that choose different mixed actions but with the same support for different types. These are called hybrid strategies.

How much cheap talk can affect the outcomes of a game is itself an interesting research topic. Interested readers are referred to the survey paper by Farrell and Rabin [4] and references therein.

These refinement concepts require additional rationality properties on beliefs, given the payoff functions. There is a different approach such that the sender’s rationality (i.e., the payoff function) is doubted, if an off-path action is observed. See Schulteis et al. [9].

This story is totally made up by the author, who did not consult either In-Koo or David on this.

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Farrell J, Rabin M (1996) Cheap talk. J Econ Perspect 10(3):103–118CrossRef

Fudenberg D, Tirole J (1991) Perfect bayesian equilibrium and sequential equilibrium. J Econ Theor 53(2):236–260MATHMathSciNetCrossRef

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Kreps D, Wilson R (1982) Reputation and imperfect information. J Econ Theor 27(2):253–279MATHMathSciNetCrossRef

Luce D, Raiffa H (1957) Games and decisions. Wiley, New YorkMATH

Schulteis T, Perea A, Peters H, Vermeulen D (2007) Revision of conjectures about the opponent’s utilities in signaling games. Econ Theor 30(2):373–384MATHMathSciNetCrossRef

Title: Perfect Bayesian Equilibrium
Author: Takako Fujiwara-Greve
Publisher: Springer Japan
Book: Non-Cooperative Game Theory
Print ISBN: 978-4-431-55644-2

Electronic ISBN: 978-4-431-55645-9

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-4-431-55645-9_7