Loyalty Rewards Facilitate Tacit Collusion

Abstract

Using a dynamic overlapping-generations model, we show that loyalty rewards robustly facilitate tacit collusion. We compare the sustainability of tacit collusion when uniform prices are used, when loyal customers are rewarded without using commitment, and when loyalty rewards are implemented by committing to offering customers either lower fixed repeat-purchase prices or fixed repeat-purchase discounts. We find that, relative to uniform prices, rewarding loyalty without using commitment on the equilibrium path makes tacit collusion easier to sustain, because a deviating firm is unable to steal one period of industry profit before losing all future profits. When loyalty rewards are offered by firms committing to repeat-purchase prices, collusion is even easier to sustain, since a deviating firm cannot renege on its discounted price for repeat-purchase customers. When firms commit to repeat-purchase discounts, they also commit to lowering the price for their repeat-purchase customers if they undercut the regular price, rendering tacit collusion to be even more readily sustainable. Our results hold whether products are homogeneous or horizontally differentiated as in a Hotelling model.