Nonasymptotic mean-field games

Nonasymptotic mean-field games

H. Tembine, Nonasymptotic mean-field games,  IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, accepted and to appear  2014.
H. Tembine
Nonasymptotic Mean-Field Games, mean-field approximation in finite regime
2014
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate  large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications.  However, the stylized game model with  continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic  regime is meaningless for networks with few entities.
In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including  dynamic auction with asymmetric valuation distributions, and spiteful bidders.
IEEE SMC