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.
|Publisher||Maastricht University, Graduate School of Business and Economics|
|Publication status||Published - 14 Aug 2018|
|Series||GSBE Research Memoranda|
- c73 - "Stochastic and Dynamic Games; Evolutionary Games; Repeated Games"
- stochastic games
- zero-sum games
- subgame φ-maxmin strategies
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