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In this paper, we present a mean field game to model the production behaviorsof a very large number of producers, whose carbon emissions are regulated bygovernment. Especially, an emission permits trading scheme is considered in ourmodel, in which each enterprise can trade its own permits flexibly. By means ofthe mean field equilibrium, we obtain a Hamilton-Jacobi-Bellman (HJB) equationcoupled with a Kolmogorov equation, which are satisfied by the adjoint stateand the density of producers (agents), respectively. Then, we propose aso-called fitted finite volume method to solve the HJB equation and theKolmogorov equation. The efficiency and the usefulness of this method areillustrated by the numerical experiments. Under different conditions, theequilibrium states as well as the effects of the emission permits price areexamined, which demonstrates that the emission permits trading schemeinfluences the producers' behaviors, that is, more populations would like tochoose a lower rather than a higher emission level when the emission permitsare expensive.

Modeling and Computation of Mean Field Equilibria in Producers' Game with Emission Permits Trading