Pull–push strategies under Cournot competition

We consider one supplier that decides 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 pull contract. We first establish the supplier’s production decision, and the manufacturers’ ordering and selling decisions, given both manufacturers’ contracting strategies, i.e., push contract or pull contract. We characterize the first-mover advantage of a push contract under competition, and find that when a competitor chooses a pull contract, the manufacturer with a push contract will possibly reduce his order quantity even when the supplier reduces supply to his competitor. Then, we investigate manufacturers’ equilibrium contracting strategies, and the supplier’s contracting preference. 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 a pull contract alone cannot achieve Pareto improvement, and only a mixed contract can possibly achieve Pareto improvement for reasonable wholesale prices.