Mean field asymptotics of Markov decision evolutionary games and teams

Tembine Hamidou, Jean Yves Le Boudec, Rachid El-Azouzi, Eitan Altman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We introduce Markov Decision Evolutionary Games with N players, in which each individual in a large population interacts with other randomly selected players. The states and actions of each player in an interaction together determine the instantaneous payoff for all involved players. They also determine the transition probabilities to move to the next state. Each individual wishes to maximize the total expected discounted payoff over an infinite horizon. We provide a rigorous derivation of the asymptotic behavior of this system as the size of the population grows to infinity. We show that under any Markov strategy, the random process consisting of one specific player and the remaining population converges weakly to a jump process driven by the solution of a system of differential equations. We characterize the solutions to the team and to the game problems at the limit of infinite population and use these to construct almost optimal strategies for the case of a finite, but large, number of players. We show that the large population asymptotic of the microscopic model is equivalent to a (macroscopic) Markov decision evolutionary game in which a local interaction is described by a single player against a population profile. We illustrate our model to derive the equations for a dynamic evolutionary Hawk and Dove game with energy level.

Original languageEnglish (US)
Title of host publicationProceedings of the 2009 International Conference on Game Theory for Networks, GameNets '09
Pages140-150
Number of pages11
DOIs
StatePublished - Oct 20 2009
Event2009 International Conference on Game Theory for Networks, GameNets '09 - Istanbul, Turkey
Duration: May 13 2009May 15 2009

Other

Other2009 International Conference on Game Theory for Networks, GameNets '09
CountryTurkey
CityIstanbul
Period5/13/095/15/09

Fingerprint

Random processes
Electron energy levels
Differential equations

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Vision and Pattern Recognition

Cite this

Hamidou, T., Le Boudec, J. Y., El-Azouzi, R., & Altman, E. (2009). Mean field asymptotics of Markov decision evolutionary games and teams. In Proceedings of the 2009 International Conference on Game Theory for Networks, GameNets '09 (pp. 140-150). [5137395] https://doi.org/10.1109/GAMENETS.2009.5137395

Mean field asymptotics of Markov decision evolutionary games and teams. / Hamidou, Tembine; Le Boudec, Jean Yves; El-Azouzi, Rachid; Altman, Eitan.

Proceedings of the 2009 International Conference on Game Theory for Networks, GameNets '09. 2009. p. 140-150 5137395.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hamidou, T, Le Boudec, JY, El-Azouzi, R & Altman, E 2009, Mean field asymptotics of Markov decision evolutionary games and teams. in Proceedings of the 2009 International Conference on Game Theory for Networks, GameNets '09., 5137395, pp. 140-150, 2009 International Conference on Game Theory for Networks, GameNets '09, Istanbul, Turkey, 5/13/09. https://doi.org/10.1109/GAMENETS.2009.5137395
Hamidou T, Le Boudec JY, El-Azouzi R, Altman E. Mean field asymptotics of Markov decision evolutionary games and teams. In Proceedings of the 2009 International Conference on Game Theory for Networks, GameNets '09. 2009. p. 140-150. 5137395 https://doi.org/10.1109/GAMENETS.2009.5137395
Hamidou, Tembine ; Le Boudec, Jean Yves ; El-Azouzi, Rachid ; Altman, Eitan. / Mean field asymptotics of Markov decision evolutionary games and teams. Proceedings of the 2009 International Conference on Game Theory for Networks, GameNets '09. 2009. pp. 140-150
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