Reward Programs and Tacit Collusion
Authors: Kim Byung-Do , Shi Mengze , Srinivasan Kannan 
Published: December 2003

Reward programs, a promotional tool to develop customer loyalty, offer incentives to consumers on the basis of cumulative purchases of a given product or service from a firm. Reward programs have become increasingly common in many industries. The best-known examples include frequent-flier programs offered by airlines, frequent-guest programs offered by hotels, and frequent-shopper programs offered by supermarkets. Despite the widespread business practice of reward programs, research efforts on reward programs, particularly in marketing, have been scarce. Our paper takes an important step towards understanding the design of reward programs and its implications on pricing strategies. We study a market that consists of two segments: heavy- and light-user segments. The key distinction between the two segments is that the heavy-user segment purchases in each period and thus is a candidate for the reward programs. In contrast, the light-user segment exits the market after one purchase and is not in a position to exploit reward programs. An important feature of our model is that we allow for different price sensitivity between heavy-user and light-user segments. Our model closely examines the type of rewards. A reward worth a dollar to the consumer might have different cost implications for the offering firm, depending on the type of reward. For example, cash rewards have higher unit reward cost (inefficient reward) for the firm than a free product of the firm, such as an airline ticket or long-distance minutes (efficient reward). Specifically, we examine an interesting puzzle observed in the marketplace. Several firms offer a cash reward or a product not made by the firm, such as jackets, electronic items, etc. These firms could offer their own product as rewards and significantly lower their cost. We examine whether there is any reason for such a seemingly suboptimal practice. Our analysis shows that reward programs weaken price competition. By offering the incentives for repeat purchases, reward programs increase a firm's cost to attract competing firms' current customers. Because firms gain less from undercutting their prices, equilibrium prices go up. Moreover, as consumers become unwilling to switch because of potential rewards, the firm with a larger market share in the heavy-user segment charges higher prices. Therefore, a low price in the first period, which leads to a larger market share in the heavy-user segment, will always be followed by a high price in the second period. In our model, consumers are rational and can correctly anticipate firms' incentive to offer lower prices initially to enroll them into the reward programs. Our paper offers an explanation as to why the type and amount of reward may vary across the programs. We identify two determining factors for the selection of rewards: size and relative price sensitivity of the heavy-user segment. We find that in a market with a small heavy-user segment that is also much more price sensitive than the light-user segment, it is optimal for firms to offer the most inefficient rewards. The intuition is based on the firms' incentive to exploit the price-insensitive light-user segment. By offering inefficient rewards, firms are able to commit to weaker competition and, therefore, higher prices. When the heavy-user segment is large or not very price sensitive, when compared to the light-user segment, competing firms should adopt the most efficient rewards to maximize their profit. This may well be the case in a number of real-world situations in which efficient rewards are quite prevalent. We also find that optimal reward amount has a negative relationship with unit reward cost. Because both firms use rewards to attract the heavy users, they tend to offer more when they adopt the more efficient rewards. Finally, our paper identifies the relationship between market characteristics and theimpact of reward programs on firms' profits and consumers' benefits. We find that firms gain from the adoption of reward programs as long as light users are not too price sensitive. When light users are very price sensitive, firms engage in intense price competition, thus benefiting little from the loyalty of heavy users created through rewards. Because reward programs increase market prices, light users, who do not get the reward, earn strictly lower benefit. In contrast, heavy users often stand to gain more from the reward program. In most cases, firms and the heavy users are better off at the expense of light users.