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 SM ISO690:2012LOZOVANU, Dmitrii. On determining stationary Nash equilibria for average single-controller stochastic games. In: Mathematics and IT: Research and Education, 1-3 iulie 2021, Chişinău. Chișinău, Republica Moldova: 2021, pp. 52-53. |
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| Mathematics and IT: Research and Education 2021 | ||||||
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Conferința "Mathematics and IT: Research and Education " Chişinău, Moldova, 1-3 iulie 2021 | ||||||
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| Pag. 52-53 | ||||||
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We consider the problem of the existence and determining stationary Nash equilibria for average single-controller stochastic games. Single-controller stochastic games with average payoffs represent a class of average stochastic games in which the transition probabilities are controlled by one player only. The problem of determining stationary Nash equilibria in such games has been studied in [2–5]. In [2, 3] has been proposed a linear programming algorithm for computing stationary equilibria in the case of two-player zero-sum games. The problem of the existence and determining stationary equilibria for a more general case of single-controlled average stochastic games has been considered in [5, 6] . We propose an approach for determining stationary Nash equilibria for single-controller stochastic games with average payoffs in general case. We show that all stationary equilibria for a single controller stochastic game can be obtained from an auxiliary noncooperative static game in normal form where the payoffs are quasi-monotonic (quasi-convex and quasi-concave) with respect to the corresponding strategies of the players and graph-continuous in the sense of Dasgupta and Maskin [1, 4]. Based on this we present a proof of the existence of stationary equilibria in a single-controller average stochastic game and propose an approach for determining the optimal stationary strategies of the players. |
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<?xml version='1.0' encoding='utf-8'?> <oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'> <dc:creator>Lozovanu, D.D.</dc:creator> <dc:date>2021</dc:date> <dc:description xml:lang='en'><p>We consider the problem of the existence and determining stationary Nash equilibria for average single-controller stochastic games. Single-controller stochastic games with average payoffs represent a class of average stochastic games in which the transition probabilities are controlled by one player only. The problem of determining stationary Nash equilibria in such games has been studied in [2–5]. In [2, 3] has been proposed a linear programming algorithm for computing stationary equilibria in the case of two-player zero-sum games. The problem of the existence and determining stationary equilibria for a more general case of single-controlled average stochastic games has been considered in [5, 6] . We propose an approach for determining stationary Nash equilibria for single-controller stochastic games with average payoffs in general case. We show that all stationary equilibria for a single controller stochastic game can be obtained from an auxiliary noncooperative static game in normal form where the payoffs are quasi-monotonic (quasi-convex and quasi-concave) with respect to the corresponding strategies of the players and graph-continuous in the sense of Dasgupta and Maskin [1, 4]. Based on this we present a proof of the existence of stationary equilibria in a single-controller average stochastic game and propose an approach for determining the optimal stationary strategies of the players.</p></dc:description> <dc:source>Mathematics and IT: Research and Education () 52-53</dc:source> <dc:title>On determining stationary Nash equilibria for average single-controller stochastic games</dc:title> <dc:type>info:eu-repo/semantics/article</dc:type> </oai_dc:dc>
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