Strategic Interactions in Marketing: A Dynamic Approach

Abstract

The aim of the thesis is to contribute to a better understanding of the strategic and dynamic interactions in some marketing problems by using a differential game approach. Specifically, in the first study, we analyze a finite time horizon advertising dynamic game under the assumption that the firms’ time preferences are time-inconsistent. Specifically, we consider two types of discounting, heterogeneous discounting and hyperbolic discounting. In the case of heterogeneous discounting, the relative importance of the final function will increase/decrease as the end of the planning horizon approaches compared with current payoffs. Whereas when agents discount future payoffs hyperbolically, their discount rates diminish rapidly in earlier stages and then slowly in the long term. We compute time-inconsistent and time-consistent feedback Nash equilibrium strategies, and compare them with those of the standard discounting case. Our results reveal that heterogeneous discounting would lead to some adapting behaviors in the last years in accordance with their increasing/decreasing valuations of the final state. Under some circumstances, the change can be so radical that the pre-commitment solution takes the contrary path of time- consistent strategies. Concerning the competition under hyperbolic discounting, different strategies exhibit disparity in the beginning, and encounter in the neighborhood in the end. Besides, a strong commitment power might induce over investment. In the second project, 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. In the third study, we consider a supply chain that faces a potential brand crisis, with one manufacturer deciding quality improvement and global advertising levels, and one retailer determining local advertising effort. The goodwill model is adopted here under the assumption that when the crisis happens, the companies suffer a sharp decrease in the goodwill. We characterize the feedback Nash equilibrium, and then we compare the corresponding quality and advertising strategies and outcomes with those of the case where the potential crises are absent, and where the

companies do not invest in quality. The effects of the instantaneous crisis rate and the short-term and long-term damages are also evaluated. Our results reveal that the pre-crisis quality improvement accelerates the goodwill build-up before the crisis, and also helps the recovery in post-crisis regime. Its twofold function suggests that one of the pre- and post-crisis regimes/instants ought to be matched with more intense investment in both quality and global advertising, depending on the overall effect of instantaneous crisis rate, short-term damage and long-term damage. This carryover effect also brings a non-monotonicity of quality improvement effort and value functions with respect to the instantaneous crisis rate. These properties leave the chance to mitigate the loss by anticipating crisis for both members under certain circumstances.