Best Response Cycles in Perfect Information Games

P. Jean-Jacques Herings*, Arkadi Predtetchinski

*Corresponding author for this work

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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 is an element of-best response cycle of length four for every is an element of> 0.

Original languageEnglish
Pages (from-to)427-433
Number of pages7
JournalMathematics of Operations Research
Issue number2
Publication statusPublished - May 2017


  • perfect information games
  • determinacy
  • best-response cycles
  • rationalizability


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