### 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 language | English (US) |
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Title of host publication | Proceedings of the 2009 International Conference on Game Theory for Networks, GameNets '09 |

Pages | 140-150 |

Number of pages | 11 |

DOIs | |

State | Published - Oct 20 2009 |

Event | 2009 International Conference on Game Theory for Networks, GameNets '09 - Istanbul, Turkey Duration: May 13 2009 → May 15 2009 |

### Other

Other | 2009 International Conference on Game Theory for Networks, GameNets '09 |
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Country | Turkey |

City | Istanbul |

Period | 5/13/09 → 5/15/09 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Computer Vision and Pattern Recognition

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Mean field asymptotics of Markov decision evolutionary games and teams

AU - Hamidou, Tembine

AU - Le Boudec, Jean Yves

AU - El-Azouzi, Rachid

AU - Altman, Eitan

PY - 2009/10/20

Y1 - 2009/10/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70349977430&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349977430&partnerID=8YFLogxK

U2 - 10.1109/GAMENETS.2009.5137395

DO - 10.1109/GAMENETS.2009.5137395

M3 - Conference contribution

AN - SCOPUS:70349977430

SN - 9781424441778

SP - 140

EP - 150

BT - Proceedings of the 2009 International Conference on Game Theory for Networks, GameNets '09

ER -