Simplifying optimal strategies in limsup and liminf stochastic games

Janos Flesch, Arkadi Predtetchinski*, William Sudderth

*Corresponding author for this work

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Abstract

We consider two-player zero-sum stochastic games with the limsup and with the liminf payoffs. For the limsup payoff, we prove that the existence of an optimal strategy implies the existence of a stationary optimal strategy. Our construction does not require the knowledge of an optimal strategy, only its existence. The main technique of the proof is to analyze the game with specific restricted action spaces. For the liminf payoff, we prove that the existence of a subgame-optimal strategy (i.e. a strategy that is optimal in every subgame) implies the existence of a subgame-optimal strategy under which the prescribed mixed actions only depend on the current state and on the state and the actions chosen at the previous period. In particular, such a strategy requires only finite memory. The proof relies on techniques that originate in gambling theory. (C) 2018 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)40-56
Number of pages17
JournalDiscrete Applied Mathematics
Volume251
Early online dateJun 2018
DOIs
Publication statusPublished - 31 Dec 2018

Keywords

  • zero-sum game
  • stochastic game
  • optimal strategy
  • stationary strategy
  • Stochastic game
  • Stationary strategy
  • Optimal strategy
  • Zero-sum game

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