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Best-Response Cycles in Perfect Information Games

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  • P. Jean-Jacques Herings

    (Department of Economics, Maastricht University, 6200 MD Maastricht, Netherlands)

  • Arkadi Predtetchinski

    (Department of Economics, Maastricht University, 6200 MD Maastricht, Netherlands)

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 of four 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

  • P. Jean-Jacques Herings & Arkadi Predtetchinski, 2017. "Best-Response Cycles in Perfect Information Games," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 427-433, May.
    • Handle: RePEc:inm:ormoor:v:42:y:2017:i:2:p:427-433
    DOI: 10.1287/moor.2016.0808
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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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