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Behavior strategies, mixed strategies and perfect recall

Abstract

When perfect recall is not satisfied, the informational contents of mixed and behavior strategies differ and are more than what the information partition describes. First, we consider two kinds of additional information strategies may carry, and show that such information leads to theperfect recall refinement of a given information partition. This does not, however, imply that the strategies compensate fully for the lack of perfect recall. We give a necessary and sufficient condition on an information partition, calledA-loss, for the informational content of mixed strategies to fully compensate for the lack of perfect recall. The informational content of behavior strategies never fully compensates.

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The authors thank Bernard Lebrun, Wen Mao, Reinhard Selten, an anonymous referee of this journal and participants in the seminars at The Australian National University, Duke University and VPI&SU for discussions and comments.

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Kaneko, M., Kline, J.J. Behavior strategies, mixed strategies and perfect recall. Int J Game Theory 24, 127–145 (1995). https://doi.org/10.1007/BF01240038

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  • DOI: https://doi.org/10.1007/BF01240038

Keywords

  • Economic Theory
  • Game Theory
  • Mixed Strategy
  • Informational Content
  • Information Strategy