Pure equilibrium strategies for stochastic games via potential functions

J.A.M. Potters, T.E.S. Raghavan, S.H. Tijs

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

Abstract

Strategic games with a potential function have quite often equilibria in pure strategies (Monderer and Shapley [4]). This is also true for stochastic games but the existence of a potential function is mostly hard to prove. For some classes of stochastic games with an additional structure, an equilibrium can be found by solving one or a finite number of finite strategic games.We call these games auxiliary games. In this paper, we investigate if we can derive the existence of equilibria in pure stationary strategies from the fact that the auxiliary games allow for a potential function. We will do this for zero-sum, two-person discounted stochastic games and non-zero-sum discounted stochastic games with additive reward functions and additive transitions (Raghavan et al. [8]) or with separable rewards and state independent transitions (Parthasarathy et al. [5]).
Original languageEnglish
Title of host publicationAdvances in Dynamic Games and their Applications
Place of PublicationBoston
PublisherBirkhauser
Pages433-444
ISBN (Print)9780817648336
Publication statusPublished - 2009

Publication series

NameAnnals of the International Society of Dynamic Games
Number10

Fingerprint

Stochastic Games
Potential Function
Game
Reward
Nonzero-sum Games
Two-person Games
Zero-sum
Strategy

Cite this

Potters, J. A. M., Raghavan, T. E. S., & Tijs, S. H. (2009). Pure equilibrium strategies for stochastic games via potential functions. In Advances in Dynamic Games and their Applications (pp. 433-444). (Annals of the International Society of Dynamic Games; No. 10). Boston: Birkhauser.
Potters, J.A.M. ; Raghavan, T.E.S. ; Tijs, S.H. / Pure equilibrium strategies for stochastic games via potential functions. Advances in Dynamic Games and their Applications. Boston : Birkhauser, 2009. pp. 433-444 (Annals of the International Society of Dynamic Games; 10).
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Potters, JAM, Raghavan, TES & Tijs, SH 2009, Pure equilibrium strategies for stochastic games via potential functions. in Advances in Dynamic Games and their Applications. Annals of the International Society of Dynamic Games, no. 10, Birkhauser, Boston, pp. 433-444.

Pure equilibrium strategies for stochastic games via potential functions. / Potters, J.A.M.; Raghavan, T.E.S.; Tijs, S.H.

Advances in Dynamic Games and their Applications. Boston : Birkhauser, 2009. p. 433-444 (Annals of the International Society of Dynamic Games; No. 10).

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

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Potters JAM, Raghavan TES, Tijs SH. Pure equilibrium strategies for stochastic games via potential functions. In Advances in Dynamic Games and their Applications. Boston: Birkhauser. 2009. p. 433-444. (Annals of the International Society of Dynamic Games; 10).