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

Janos Flesch, P. Jean-Jacques Herings, Jasmine Maes and Arkadi Predtetchinski
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Janos Flesch: QE Math. Economics & Game Theory, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation
Jasmine Maes: Microeconomics & Public Economics, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation

No 20, Research Memorandum from Maastricht University, Graduate School of Business and Economics (GSBE)

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.

JEL-codes: C73 (search for similar items in EconPapers)
Date: 2018-08-14
New Economics Papers: this item is included in nep-gth
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Journal Article: Subgame Maxmin Strategies in Zero-Sum Stochastic Games with Tolerance Levels (2021) Downloads
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DOI: 10.26481/umagsb.2018020

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