The Strategic Impact of Higher-Order Beliefs

49 Pages Posted: 7 Sep 2012

See all articles by Yi-Chun Chen

Yi-Chun Chen

National University of Singapore (NUS) - Department of Economics

Alfredo Di Tillio

Bocconi University - Department of Economics

Eduardo Faingold

Insper Institute of Education and Research

Siyang Xiong

Rice University - Department of Economics

Date Written: September 6, 2012

Abstract

Previous research has established that the predictions made by game theory about strategic behavior in incomplete information games are quite sensitive to the assumptions made about the players’ infinite hierarchies of beliefs. We evaluate the severity of this robustness problem by characterizing conditions on the primitives of the model — the players’ hierarchies of beliefs — for the strategic behavior of a given Harsanyi type to be approximated by the strategic behavior of (a sequence of) perturbed types. This amounts to providing characterizations of the strategic topologies of Dekel, Fudenberg, and Morris (2006) in terms of beliefs. We apply our characterizations to a variety of questions concerning robustness to perturbations of higher-order beliefs, including genericity of common priors, and the connections between robustness of strategic behavior and the notion of common p-belief of Monderer and Samet (1989).

Keywords: Games with incomplete information, Rationalizability, Higher-order beliefs, Robustness

JEL Classification: C70, C72

Suggested Citation

Chen, Yi-Chun and Di Tillio, Alfredo and Faingold, Eduardo and Xiong, Siyang, The Strategic Impact of Higher-Order Beliefs (September 6, 2012). Cowles Foundation Discussion Paper No. 1875. Available at SSRN: https://ssrn.com/abstract=2142497 or http://dx.doi.org/10.2139/ssrn.2142497

Yi-Chun Chen

National University of Singapore (NUS) - Department of Economics ( email )

1 Arts Link AS2 #06-02
Singapore 117570, Singapore 119077
Singapore

Alfredo Di Tillio

Bocconi University - Department of Economics ( email )

Milan
Italy

HOME PAGE: http://mypage.unibocconi.eu/alfredoditillio

Eduardo Faingold (Contact Author)

Insper Institute of Education and Research ( email )

R Quata 300
Sao Paulo, 04542-030
Brazil

HOME PAGE: http://www.eduardofaingold.com

Siyang Xiong

Rice University - Department of Economics ( email )

6100 South Main Street
Houston, TX 77005
United States

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