On the Existence and Determining Stationary Nash Equilibria for Switching Controller Stochastic Games

Authors

  • Dmitrii Lozovanu Institute of Mathematics and Computer Science of Moldova Academy of Sciences, Academiei 5, Chisinau, MD-2028, Moldova https://orcid.org/0000-0002-5953-570X
  • Stefan Pickl Institute for Theoretical Computer Science, Mathematics and Operations Research, Universitat der Bundeswehr Munchen, 85577 Neubiberg-Munchen, Germany

DOI:

https://doi.org/10.21638/11701/spbu31.2021.21

Abstract

In this paper we consider the problem of the existence and determining stationary Nash equilibria for switching controller stochastic games with discounted and average payoffs. The set of states and the set of actions in the considered games are assumed to be finite. For a switching controller stochastic game with discounted payoffs we show that all stationary equilibria can be found by using an auxiliary continuous noncooperative static game in normal form in which the payoffs are quasi-monotonic (quasi-convex and quasi-concave) with respect to the corresponding strategies of the players. Based on this we propose an approach for determining the optimal stationary strategies of the players. In the case of average payoffs for a switching controller stochastic game we also formulate an auxiliary noncooperative static game in normal form with quasi-monotonic payoffs and show that such a game possesses a Nash equilibrium if the corresponding switching controller stochastic game has a stationary Nash equilibrium.

Keywords:

Stochastic game, Switching control, Stationary strategies, Stationary Nash equilibrium

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References

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Published

2021-10-30

How to Cite

Lozovanu, D., & Pickl, S. (2021). On the Existence and Determining Stationary Nash Equilibria for Switching Controller Stochastic Games. Contributions to Game Theory and Management, 14, 290–301. https://doi.org/10.21638/11701/spbu31.2021.21

Issue

Vol. 14 (2021)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.