@techreport{13c4e5cefdf34625b358b242a72cbe22,
title = "Subgame maxmin strategies in zero-sum stochastic games with tolerance levels",
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. ",
keywords = "stochastic games, zero-sum games, subgame φ-maxmin strategies",
author = "Janos Flesch and Herings, {P. Jean-Jacques} and Jasmine Maes and Arkadi Predtetchinski",
year = "2018",
month = aug,
day = "14",
doi = "10.26481/umagsb.2018020",
language = "English",
series = "GSBE Research Memoranda",
publisher = "Maastricht University, Graduate School of Business and Economics",
number = "020",
address = "Netherlands",
type = "WorkingPaper",
institution = "Maastricht University, Graduate School of Business and Economics",
}