Hierarchies of Belief and Interim Rationalizability

CMS-EMS Northwestern University Working Paper No. 1388

46 Pages Posted: 5 Dec 2004

See all articles by J.C. Ely

J.C. Ely

Northwestern University - Department of Economics

Marcin Peski

University of Texas at Austin

Date Written: November 2004

Abstract

In games with incomplete information, conventional hierarchies of belief are incomplete as descriptions of the players' information for the purposes of determining a player's behavior. We show by example that this is true for a variety of solution concepts. We then investigate what is essential about a player's information to identify rationalizable behavior in any game. We do this by constructing the universal type space for rationalizability and characterizing the types in terms of their beliefs. Infinite hierarchies of beliefs over conditional beliefs, what we call delta-hierarchies, are what turn out to matter. We show that any two types in any two type spaces have the same rationalizable sets in all games if and only if they have the same delta-hierarchies.

Keywords: Hierarchies of belief, rationalizability, bayesian games, incomplete information

JEL Classification: C73, D83

Suggested Citation

Ely, Jeffrey C. and Peski, Marcin, Hierarchies of Belief and Interim Rationalizability (November 2004). CMS-EMS Northwestern University Working Paper No. 1388. Available at SSRN: https://ssrn.com/abstract=626641 or http://dx.doi.org/10.2139/ssrn.626641

Jeffrey C. Ely (Contact Author)

Northwestern University - Department of Economics ( email )

2003 Sheridan Road
Evanston, IL 60208
United States
847-491-8219 (Phone)

Marcin Peski

University of Texas at Austin ( email )

2317 Speedway
Austin, TX 78712
United States

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