A model of coalition reward programs

Abstract

A coalition reward program is a joint reward program that links multiple brands in a partnership, such that consumers who make a purchase from a brand in the coalition earn a reward that is redeemable across the brands. However, despite the increasing prevalence of such programs, there have been some failures and setbacks in recent years. One famous example is the Plenti loyalty program, which announced its demise only three years after its launch. Plenti linked a remarkably wide variety of brands, including Macy's, Chili's, and AT&T, most of which now offer proprietary reward programs. This leads to the following questions: why did these brands return to proprietary reward programs? Which type of program is more effective for building customer loyalty and increasing firm profit: a proprietary reward program or a coalition reward program? Moreover, as coalition reward programs typically differ greatly in size, how can the optimal size be determined, and how does the size of a coalition affect its effectiveness? This thesis will study the optimal design of coalition reward programs, whether joining a coalition benefits a firm, and how the size affects its effectiveness. To this end, we will start with the simplest case: a coalition reward program consisting of n independent and symmetric firms, each of which sells a non-durable product to infinitesimal customers over an infinite horizon. Time is continuous, and a customer visits each firm following a Poisson process at a rate λ. Thus, a customer visits the coalition at a rate nλ. Any purchase from a firm in the coalition earns the customer a reward that can be redeemed across the firms before the reward expires. The coalition manager chooses the price, the reward, the expiration term, and the size n to maximize the program's long-term average revenue. We will use continuous-time dynamic programming to analyze the customer's decision problem for a given coalition program, in which the state represents whether the customer holds a valid reward when she visits the coalition. We will analyze the coalition's optimal decisions based on the customer's optimal behavior, and compare the coalition's profit with that of the proprietary reward program. Finally, we will investigate how to determine the optimal size. Overall, this thesis will study coalition reward programs from the perspective of operations management by determining the optimal design of the programs and developing an improved understanding of the rationale and effectiveness of such programs.