An Approach for Determining Stationary Equilibria in a Single-Controller Average Stochastic Game
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LOZOVANU, Dmitrii; PICKL, Stefan Wolfgang. An Approach for Determining Stationary Equilibria in a Single-Controller Average Stochastic Game. In: Trends in Mathematics. 11 octombrie 2021, Berlin. Berlin, Germania: Springer Science and Business Media Deutschland GmbH, 2021, pp. 235-250.
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Trends in Mathematics 2021
Sesiunea "Trends in Mathematics"
Berlin, Germany, 11 octombrie 2021

An Approach for Determining Stationary Equilibria in a Single-Controller Average Stochastic Game

DOI: https://doi.org/10.1007/978-3-030-93616-7_13

Pag. 235-250

Lozovanu Dmitrii1, Pickl Stefan Wolfgang2
 
1 Vladimir Andrunachievici Institute of Mathematics and Computer Science,
2 Bundeswehr University Munich
 
Disponibil în IBN: 8 aprilie 2022


Rezumat

In this paper the problem of the existence and determining stationary Nash equilibria in a single-controller average stochastic game is considered. The set of states and the set of actions in the game are assumed to be finite. We show that all stationary equilibria for such a 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. 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.