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Contributions to Game Theory and Management, 2019, Volume 12, Pages 246–260
(Mi cgtm346)
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This article is cited in 1 scientific paper (total in 1 paper)
Pure stationary nash equilibria for discounted stochastic positional games
Dmitrii Lozovanua, Stefan Picklb a Institute of Mathematics and Computer Science of Moldova Academy of Sciences, Academiei 5, Chisinau, MD-2028, Moldova
b Institute for Theoretical Computer Science, Mathematics and Operations Research, Universität der Bundeswehr München, 85577 Neubiberg-München, Germany
Abstract:
A discounted stochastic positional game is a stochastic game with
discounted payoffs in which the set of states is divided into
several disjoint subsets such that each subset represents the
position set for one of the player and each player control the
Markov decision process only in his position set. In such a game
each player chooses actions in his position set in order to
maximize the expected discounted sum of his stage rewards. We show
that an arbitrary discounted stochastic positional game with finite
state and action spaces possesses a Nash equilibrium in pure
stationary strategies. Based on the proof of this result we present
conditions for determining all optimal pure stationary strategies of
the players.
Keywords:
stochastic positional games, discounted payoffs, pure stationary strategies, mixed stationary strategies, Nash equilibria.
Citation:
Dmitrii Lozovanu, Stefan Pickl, “Pure stationary nash equilibria for discounted stochastic positional games”, Contributions to Game Theory and Management, 12 (2019), 246–260
Linking options:
https://www.mathnet.ru/eng/cgtm346 https://www.mathnet.ru/eng/cgtm/v12/p246
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