Abstract
In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize their average cost by choosing their trading rates with a price that is characterized by a balance between supply and demand. The supply and the price processes are assumed to follow stochastic differential equations. Here, we show that, for linear dynamics and quadratic costs, the optimal trading rates are determined in feedback form. Hence, the price arises as the solution to a stochastic differential equation, whose coefficients depend on the solution of a system of ordinary differential equations.
Highlights
Mean-field games (MFG) is a tool to study the Nash equilibrium of infinite populations of rational agents
In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations
Agents seek to minimize their average cost by choosing their trading rates with a price that is characterized by a balance between supply and demand
Summary
Mean-field games (MFG) is a tool to study the Nash equilibrium of infinite populations of rational agents. We study a price formation model for a commodity traded in a market under uncertain supply, which is a common noise shared by the agents. These agents are rational and aim to minimize the average trading cost by selecting their trading rate. The price is determined by a market-clearing condition that ensures that supply meets demand This approach avoids the use of the master equation.
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