An analysis of efficiency of time-consistent coordination mechanisms in a model of supply chain management

Abstract

In this paper, we study an advertising dynamic game in supply chain management under the assumption that the agents differ in their time preference rates. We study two coordination mechanisms: the cost sharing program, where the retailer can get some reimbursement of the advertising cost from the manufacturer; and the vertical integration, where the two players aim to maximize the joint profit. We derive the time-consistent cooperative advertising strategies in each coordination setting, and we compare them with the non-cooperative case. Our results show that, the cost sharing program is Pareto superior to the non-cooperative setting, while vertical integration could be more preferred by the manufacturer and less preferred by the retailer if the initial goodwill level is sufficiently high. Besides, unlike previous results in the literature, we found that when the agents' discount rates are very different, joint profits could be lower under vertical integration than in the non-cooperative case, which yields an inefficient cooperation.