Average-discounted equilibria in stochastic games
type: Item
instance of: scholarly article
title: Average-discounted equilibria in stochastic games
zbMATH Open document ID: 0945.91005
DOI: 10.1016/S0377-2217(97)00384-6
author: Frank Thuijsman
author: K. Vrieze
author: János Flesch
published in: European Journal of Operational Research
publication date: 2000-10-05T00:00:00Z
review text: Stochastic two-person non-zero-sum games with finite state and action spaces are examined when player 1 is interested in the limiting average, player 2 in the \(\beta\)-discounted reward. By the nature of these rewards, player 1's reward emphasizes what happens in the far, player 2's in the near future. It can be proved that for all \(\varepsilon>0\) and all \(\beta\in(0,1)\), there exists a stationary Nash \(\varepsilon\)-equilibrium. The same result holds within the class of ultimately stationary strategies, i.e. that the players play up to some stage \(N\) Markov and after it stationary strategies. An example is given what demonstrates that 0-equilibria do not necessarily exist, not even in terms of history-dependent strategies. However, in some classes of stochastic games with special transition and payoff structures (unichain, perfect information switching control, ARAT, repeated games with absorbing states), (\(\varepsilon\)-)equilibria can be achieved.
Mathematics Subject Classification ID: 91A15
zbMATH DE Number: 1358461
zbMATH Keywords: stochastic game
zbMATH Keywords: average-discounted equilibrium
MaRDI profile type: Publication
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cites work: Weighted reward criteria in Competitive Markov Decision Processes
cites work: Q5331697
cites work: Q3245641
cites work: A generalization of Brouwer's fixed point theorem
cites work: Stochastic Games with Perfect Information and Time Average Payoff
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cites work: Q5342876
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description: scientific article; zbMATH DE number 1358461