Best-Response Cycles in Perfect Information Games

P. Jean-Jacques Herings and Arkadi Predtetchinski ()
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Arkadi Predtetchinski: Department of Economics, Maastricht University, 6200 MD Maastricht, Netherlands

Mathematics of Operations Research, 2017, vol. 42, issue 2, 427-433

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.

Keywords: perfect information games; determinacy; best-response cycles; rationalizability (search for similar items in EconPapers)
Date: 2017
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https://doi.org/10.1287/moor.2016.0808 (application/pdf)

Related works:
Working Paper: Best response cycles in perfect information games (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:42:y:2017:i:2:p:427-433

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