Price Discrimination with Fairness Constraints

Price discrimination strategies, which offer different prices to customers based on differences in their valuations, have become common practice. Although it allows sellers to increase their profits, it also raises several concerns in terms of fairness (e.g., by charging higher prices (or denying access) to protected minorities in case they have higher (or lower) valuations than the general population). This topic has received extensive attention from media, industry, and regulatory agencies. In this paper, we consider the problem of setting prices for different groups under fairness constraints. We first propose four definitions: fairness in price, demand, consumer surplus, and no-purchase valuation. We prove that satisfying more than one of these fairness constraints is impossible even under simple settings. We then analyze the pricing strategy of a profit-maximizing seller and the impact of imposing fairness on the seller's profit, consumer surplus, and social welfare. Under a linear demand model, we find that imposing a small amount of price fairness increaces social welfare, whereas too much price fairness may result in a lower welfare relative to imposing no fairness. On the other hand, imposing fairness in demand or consumer surplus always decreases social welfare. Finally, no-purchase valuation fairness always increases social welfare. We observe similar patterns under several extensions and for other common demand models numerically. Our results and insights provide a first step in understanding the impact of imposing fairness in the context of discriminatory pricing.