Dynamic Cournot Games of Energy Production under Constant Prudence Price Functions

Abstract

The ongoing COVID-19 crisis has had an especially pernicious impact on the energy market, as worldwide lockdown measures and the ensuing war between oil superpowers Russia and OPEC have led to an unprecedented drop in oil prices in April 2020. Energy producers are now struggling to recover from the shocks in supply and demand that have destabilized the market. This underlies a need for firms to anticipate future price volatility in planning out their strategies. The recent developments in energy pricing motivate our study of commodity markets modeled as dynamic Cournot games, where the market demand and producers' inventories are governed by stochastic processes. We introduce the game theoretic framework of $N$-player continuous-time Cournot games, where firms choose production quantities at each time period to maximize their individual profit. The production side of the market consists of both fossil fuel-based (i.e. exhaustible) and renewable (inexhaustible) energy producers who maximize their value functions characterized by a system of nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equations. The unique market price of this economic game is given by a constant prudence price function, where the prudence coefficient takes values in $[0, 2)$. We characterize the market price volatility for different oligopoly patterns, both analytically and through numerical simulation. This allows us to compare the price volatility curves for different values of the constant prudence coefficient, which reflects the changes in market structure due to consumers' varying willingness to invest in energy services in the face of market uncertainty.