Template-type: ReDif-Paper 1.0
Author-Name: Flesch, Janos
Author-workplace-name: QE Math. Economics & Game Theory, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation
Author-Name: Herings, P. Jean-Jacques
Author-workplace-name: Microeconomics & Public Economics, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation, RS: GSBE Theme Data-Driven Decision-Making
Author-Name: Maes, Jasmine
Author-workplace-name: Microeconomics & Public Economics, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation
Author-Name: Predtetchinski, Arkadi
Author-workplace-name: Microeconomics & Public Economics, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation
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. 
Classification-JEL: c73
Series: GSBE Research Memoranda
Creation-Date: 20180814
Number: 020
File-URL: https://cris.maastrichtuniversity.nl/ws/files/27587143/RM18020.pdf
File-Format: application/pdf
File-Size: 700874
Handle: Repec:unm:umagsb:2018020
DOI: 10.26481/umagsb.2018020