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.