 Computing equilibria in discounted dynamic gamesAndriy Burkov and Brahim Chaib-draa Applied Mathematics and Computation, 2015, vol. 269, issue C, 863-884 Abstract: Game theory (GT) is an essential formal tool for interacting entities; however computing equilibria in GT is a hard problem. When the same game can be played repeatedly over time, the problem becomes even more complicated. The existence of multiple game states makes the problem of computing equilibria in such games extremely difficult. In this paper, we approach this problem by first proposing a method to compute a nonempty subset of approximate (up to any precision) subgame-perfect equilibria in repeated games. We then demonstrate how to extend this method to approximate all subgame-perfect equilibria in a repeated game, and also to solve more complex games, such as Markov chain games and stochastic games. We observe that in stochastic games, our algorithm requires additional strong assumptions to become tractable, while in repeated and Markov chain games it allows approximating all subgame-perfect equilibria reasonably fast and under considerably weaker assumptions than previous methods. Keywords: Game theory; Repeated games; Stochastic games; Markov chain games; Subgame-perfect equilibria; Automaton (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:269:y:2015:i:c:p:863-884 DOI: 10.1016/j.amc.2015.07.068 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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