Cooperative advertising: A way escaping from the prisoner’s dilemma in a supply chain with sticky price

Abstract

This paper develops a differential game in a two-player supply chain with sticky price where a manufacturer provides a cooperative advertising program for a retailer. The manufacturer sets the wholesale price while the retailer decides the order quantity and advertising level. Either of the players has two behavioral choices: Myopia and farsightedness. We derive and compare the equilibrium strategies under four different behavioral combinations of the two players. Our analysis shows that, to be farsighted is the equilibrium behavior-choice result for the manufacturer and the retailer, while either of the players prefers a myopic partner. When the marginal contribution of the advertising to the notional price is low, instead of the farsighted equilibrium behavior, both players achieve the Pareto optimality when acting myopically, which traps them into a prisoner’s dilemma. Meanwhile, the myopia of both players is most desirable for the whole supply chain. When both the advertising’s marginal contribution to the notional price and the advertising subsidy rate are sufficiently high, not only can the players escape from the prisoner’s dilemma, but also their farsighted behavior-choice equilibrium can make them realize the Pareto optimality. Furthermore, a low degree of price stickiness helps the players escape from the prisoner’s dilemma and achieve their Pareto optimality at the farsighted equilibrium more easily, and a negotiated advertising subsidy rate enlarges this benefit.