Subgame maxmin strategies in zero-sum stochastic games with tolerance levels

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Abstract

We study subgame φ-maxmin strategies in two-player zero-sum stochastic games with finite action spaces and a countable state space. Here φ denotes the tolerance function, a function which assigns a non-negative tolerated error level to every subgame. Subgame φ-maxmin strategies are strategies of the maximizing player that guarantee the lower value in every subgame within the subgame-dependent tolerance level as given by φ. First, we provide necessary and sufficient conditions for a strategy to be a subgame φ-maxmin strategy. As a special case we obtain a characterization for subgame maxmin strategies, i.e. strategies that exactly guarantee the lower value at every subgame. Secondly, we present sufficient conditions for the existence of a subgame φ-maxmin strategy. Finally, we show the possibly surprising result that the existence of subgame φ-maxmin strategies for every positive tolerance function φ is equivalent to the existence of a subgame maxmin strategy.
Original languageEnglish
PublisherMaastricht University, Graduate School of Business and Economics
DOIs
Publication statusPublished - 14 Aug 2018

Publication series

SeriesGSBE Research Memoranda
Number020

JEL classifications

  • c73 - "Stochastic and Dynamic Games; Evolutionary Games; Repeated Games"

Keywords

  • stochastic games
  • zero-sum games
  • subgame φ-maxmin strategies

Cite this

Flesch, J., Herings, P. J-J., Maes, J., & Predtetchinski, A. (2018). Subgame maxmin strategies in zero-sum stochastic games with tolerance levels. Maastricht University, Graduate School of Business and Economics. GSBE Research Memoranda, No. 020 https://doi.org/10.26481/umagsb.2018020