Best Response Cycles in Perfect Information Games

13 Pages Posted: 23 Jun 2015

Date Written: May 11, 2015

Abstract

We consider n–player perfect information games with payoff functions having a finite image. We do not make any further assumptions, so in particular we refrain from making assumptions on the cardinality or the topology of the set of actions and assumptions like continuity or measurability of payoff functions. We show that there exists a best response cycle of length four, that is, a sequence (σ0, σ1, σ2, σ3, σ0) of pure strategy profiles where every successive element is a best response to the previous one. This result implies the existence of point-rationalizable strategy profiles. When payoffs are only required to be bounded, we show the existence of an ϵ–best response cycle of length four for every ϵ > 0.

Keywords: Perfect information games, determinacy, best response cycles, rationalizability

JEL Classification: C72

Suggested Citation

Herings, P. Jean-Jacques and Predtetchinski, Arkadi, Best Response Cycles in Perfect Information Games (May 11, 2015). Available at SSRN: https://ssrn.com/abstract=2621979 or http://dx.doi.org/10.2139/ssrn.2621979

P. Jean-Jacques Herings (Contact Author)

Tilburg University ( email )

Department of Econometrics and Operations Research
P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4668797 (Phone)
5000 LE (Fax)

HOME PAGE: http://https://sites.google.com/view/jean-jacques-herings/home

Arkadi Predtetchinski

Maastricht University ( email )

Tongersestraat 53
Maastricht, 6200 MD
Netherlands
+31 43 388 3906 (Phone)

HOME PAGE: http://www.personeel.unimaas.nl/a.predtetchinski/

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