Abstract: Two identical firms compete with price as the strategic variable in a homogeneous product duopoly game. The firms are limited by capacity constraints, and an efficient rationing rule is adopted. We show that when the firms are symmetric and have a small capacity, there is a unique subgame perfect Nash equilibrium, in which they both sell up to their capacity and get the same payoff. In another certain capacity range, the follower will adopt the same price with the leader, and there is a second mover advantage. We analyze an asymmetric case and attain the equilibrium. The example analysis indicates that price competition is based on the large enough capacity, and the follower should enter the market when the leader has a relatively larger capacity.

Key words: Stackelberg equilibrium, price, capacity constraints