A mean field game price model with noise

In this paper, we propose a mean-field game model for the price formation of commodity whose production is subjected to random fluctuations. The generalizes existing deterministic models. Agents seek minimize their average cost by choosing trading rates with that characterized balance between supply and demand. processes are assumed follow stochastic differential equations. Here, show that, linear dynamics quadratic costs, optimal determined in feedback form. Hence, arises as solution equation, coefficients depend on system ordinary