A theory of dynamic oligopoly, III. Cournot competition

We study the Markov perfect equilibrium (MPE) of an alternating move, infinite horizon duopoly model where the strategic variable is quantity. We exhibit a pair of difference-differential equations that, when they exist, differentiable MPE strategies satisfy. For quadratic payoff functions, we solve these equations in closed form and demonstrate that the MPE corresponding to the solution is the limit of the finite horizon equilibrium as the horizon tends to infinity. We conclude with a discussion of adjustment costs and endogenization of the timing.