Incentives in Dynamic Duopoly

Abstract

We compare steady states of open loop and locally stable Markov perfect equilibria (MPE) in a general symmetric differential game duopoly model with costs of adjustment. Strategic incentives depend on whether an increase in the state variable of a firm hurts or helps the rival and on whether there is intertemporal strategic substitutability or complementarity at the MPE. Furthermore, we characterize completely strategic incentives in the linear-quadratic specification of the model and find that when production (price) is costly to adjust there is intertemporal strategic substitutability (complementarity) and the steady state of the Markov perfect equilibrium is more (less) competitive than the steady state of the open-loop equilibrium, which coincides with the static outcome. In particular, in a differentiated product duopoly market with price competition and costly production adjustment, each firm's leadership attempts turn into Stackelberg price warfare, yielding a MPE steady state outcome more competitive than static Bertrand competition. The static strategic complementarity in the price game is turned into intertemporal strategic substitutability.

Keywords: Adjustment costs, Bertrand, Cournot, differential game, Markov perfect equilibrium, open-loop equilibrium, product differentation, Stackelberg warfare point

JEL Classification: C73