Equilibrium Pull-Push Strategies under Cournot Competition

Abstract

We consider one supplier endogenously deciding the production quantity to serve two manufacturers, who contract with the supplier for raw materials and sell their finished products to the same uncertain market under Cournot competition. The manufacturers can either contract with the supplier by push contract or by pull contract. We first establish the supplier's production decision, the manufacturers' ordering and selling decisions, given both manufacturers' contracting strategies, i.e., push contract or pull contract. We characterize the first-move advantage of push contract under competition, and find that when his competitor chooses pull contract, the manufacturer with push contract will possibly reduce his order quantity even when the supplier reduces supply to his competitor. Then, we investigate the equilibria of manufacturers' contracting strategy, and the preference of the supplier. Interestingly, we find that completely symmetric manufacturers can choose different contracting strategies even when the wholesale prices for both contracts are identical. At last, we numerically characterize how competition influences the value of pull and push contracts. From the perspective of the whole supply chain, we find that pull contract alone cannot achieve Pareto improvement, and only mixed contract can possibly achieve Pareto improvement for reasonable wholesale prices.

Keywords: cournot competition; demand uncertainty; supply risk; advance reservation; regular reservation