Dynamic Cournot Models for Production of Exhaustible Commodities Under Stochastic Demand
20 Pages Posted: 21 Mar 2014
Date Written: February 21, 2014
We extend the dynamic Cournot model of Ludkovski and Sircar (2012) by considering stochastic demand. We analyze a duopoly between an exhaustible producer and a "green" competitor. Both producers dynamically make decisions regarding their production rates; in addition the exhaustible producer optimizes search for new reserves. The aggregate price earned by the producers switches between high and low demand regimes with exogenously given holding rates. We study how the regime changes and the amount of competition affect game equilibria, and compare with the case of deterministic demand. A novel feature driven by stochasticity of demand is that production may shut down during low demand to conserve reserves.
Keywords: Cournot games, exploration control, stochastic demand, stochastic differential games, exhaustible resources
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