How do loyalty programs affect goodwill? An optimal control approach

This paper examines the long-term impact of loyalty programs on a company’s profit and reputation among customers, and with different durations of product use. We analyze how the launch of loyalty programs may change the profitability of optimal advertising activities. The basis of this study is a modified goodwill model where the market is segmented according to usage experience. The main novelty is the role of loyalty programs and consumer recommendations in the creation of product goodwill, and also their influence on optimal advertising. The dynamics of goodwill are described by a partial differential equation. The firm maximizes the sum of discounted profits by choosing a different advertising campaign for each market segment. For a high-quality product, we observe that there is a trade off between the loyalty program and optimal advertising strategies. For a low-quality product, the loyalty program causes more profitable companies to invest heavily in additional advertising efforts.The authors gratefully acknowledge financial support from the National Science Centre in Poland. Decision number: DEC-2011/03/D/HS4/04269

Investigating the role of customer churn in the optimal allocation of offensive and defensive advertising: the case of the competitive growing market

The paper investigates the optimal allocation between defensive and offensive advertising efforts in a dynamic, growing market in which two companies are competing for market share. The study described in this paper extends the existing literature on dynamic advertising competition by considering a market that is in the growth phase and by including the heterogeneous decay rate of market share. A modified Lanchester is employed to describe the dynamics of market share by model. The goal of companies operating in this domain is to maximize their profits over a finite decision horizon. Based on the differential game approach the Markovian Nash strategies for offensive and defensive advertising activities are determined. Additionally, an analysis of the extent to which this solution is sensitive to changes in potential market and the rate of customer churn is made