Paying social costs to gain discounts: Is it beneficial for you?

We study two prevalent business strategies: collective buying and referral reward strategies, leveraging social interactions among consumers to incentivize purchases through discounts or rewards. Consumers exhibit heterogeneity in their awareness of the product. Aware consumers pursue discounts or rewards by inviting their peers, which can increase the unaware peers' valuation of this product. In the collective buying strategy, the retailer determines both individual purchase prices and collective buying discounts. Consumers have the option to make individual purchases or form groups. The final demand is contingent on the equilibrium of a Nash game, in which consumers form groups through invitations. In equilibrium, the optimal collective buying strategy proves to be more profitable than the posted price strategy (where consumers can only purchase individually) when the social cost of inviting is moderate, the fraction of aware consumers is not overly large, and the additional value is not negligible. Notably, the lowest collective buying discount arises when the social cost, the fraction of aware consumers, and the additional value are all at moderate levels. In the referral reward strategy, the retailer determines both individual purchase prices and rewards for successful recommendations. We derive the optimal referral reward strategy and further scrutinize the optimal retail strategy by comparing the posted price strategy, collective buying strategy, and referral reward strategy. Our comprehensive analysis reveals non-monotonic shifts in the optimal retail strategy as various parameters change, some of which appear to be novel and unreported in the existing literature. Finally, we extend our collective-buying model to address a scenario where the social cost and consumers' valuations are continuous.