Positive zero-sum stochastic games with countable state and action spaces

Janos Flesch; Arkadi Predtetchinski; William Sudderth

doi:10.1007/s00245-018-9536-3

Positive zero-sum stochastic games with countable state and action spaces

Janos Flesch
, Arkadi Predtetchinski^*
, William Sudderth

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

A positive zero-sum stochastic game with countable state and action spaces is shown to have a value if, at every state, at least one player has a finite action space. The proof uses transfinite algorithms to calculate the upper and lower values of the game. We also investigate the existence of (epsilon-)optimal strategies in the classes of stationary and Markov strategies.

Original language	English
Pages (from-to)	499-516
Number of pages	18
Journal	Applied Mathematics and Optimization
Volume	82
Issue number	2
Early online date	1 Nov 2018
DOIs	https://doi.org/10.1007/s00245-018-9536-3
Publication status	Published - 2020

Keywords

Fixed point
Markov strategy
Tarski fixed point theorem
Transfinite algorithm
optimal strategy
value of the game
zero-sum stochastic game
Optimal strategy
Zero-sum stochastic game
Value of the game
STRATEGIES

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10.1007/s00245-018-9536-3Licence: CC BY

Cite this

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abstract = "A positive zero-sum stochastic game with countable state and action spaces is shown to have a value if, at every state, at least one player has a finite action space. The proof uses transfinite algorithms to calculate the upper and lower values of the game. We also investigate the existence of (epsilon-)optimal strategies in the classes of stationary and Markov strategies.",

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AB - A positive zero-sum stochastic game with countable state and action spaces is shown to have a value if, at every state, at least one player has a finite action space. The proof uses transfinite algorithms to calculate the upper and lower values of the game. We also investigate the existence of (epsilon-)optimal strategies in the classes of stationary and Markov strategies.

KW - Fixed point

KW - Markov strategy

KW - Tarski fixed point theorem

KW - Transfinite algorithm

KW - optimal strategy

KW - value of the game

KW - zero-sum stochastic game

KW - Optimal strategy

KW - Zero-sum stochastic game

KW - Value of the game

KW - STRATEGIES

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DO - 10.1007/s00245-018-9536-3

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SN - 0095-4616

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JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

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ER -

Positive zero-sum stochastic games with countable state and action spaces

Abstract

Keywords

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