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Best response cycles in perfect information games

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  • Herings, P.J.J.

    (Microeconomics & Public Economics)

  • Predtetchinski, A.

    (Microeconomics & Public Economics)

Abstract

We consider n-player perfect information games with payofffunctions 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 payofffunctions. 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.

Suggested Citation

  • Herings, P.J.J. & Predtetchinski, A., 2015. "Best response cycles in perfect information games," Research Memorandum 017, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2015017
    DOI: 10.26481/umagsb.2015017
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    References listed on IDEAS

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    1. Martin Dufwenberg & Mark Stegeman, 2002. "Existence and Uniqueness of Maximal Reductions Under Iterated Strict Dominance," Econometrica, Econometric Society, vol. 70(5), pages 2007-2023, September.
    2. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    3. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
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