Dynamic Cournot duopoly with intertemporal capacity constraints

Abstract

This paper studies a dynamic Cournot duopoly in which suppliers have a limited amount of products available for two consecutive periods. We derive optimal sales strategies and analyze welfare effects with and without commitment. Under commitment, strategies do not depend on the rival's realized sales. In this case, there is a unique Nash equilibrium for any allocation of initial supplies and prices increase over time. Absent commitment, sellers can adjust their supply decision after the first period. In this case, a subgame perfect Nash equilibrium does not always exist and prices may decline over time. A more asymmetric allocation of stocks generally leads to higher first-period prices, whereas the impact on second-period prices is ambiguous. The larger firm typically prefers not to commit, whereas the smaller firm is better off under commitment. Commitment generates a higher total surplus and (almost always) a higher consumer surplus. Our findings thus suggest that market transparency or flexible supply contracts can adversely affect welfare in situations where production precedes sales and firms face an intertemporal capacity constraint.