Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
A Generic Mean Field Convergence Result for Systems of Interacting Objects
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
A class of mean field interaction models for computer and communication systems
Performance Evaluation
Markov decision evolutionary games with time average expected fitness criterion
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
From mean field interaction to evolutionary game dynamics
WiOPT'09 Proceedings of the 7th international conference on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
A mean field model of work stealing in large-scale systems
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Dynamic bargaining solutions for opportunistic spectrum access
WD'09 Proceedings of the 2nd IFIP conference on Wireless days
Large-scale games in large-scale systems
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Mean field stochastic games for SINR-based medium access control
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Mean field equilibria of dynamic auctions with learning
ACM SIGecom Exchanges
Distributed control of multi-agent systems with random parameters and a major agent
Automatica (Journal of IFAC)
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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.