Paper Session 17
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Price Discrimination with Fairness Constraints
Price Discrimination -- offering different prices to different customers -- has become common practice. While it allows sellers to increase their profits, it also raises several concerns in terms of fairness. 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 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 linear or exponential demand, we show that imposing a small amount of fairness in price or no-purchase valuation increases social welfare, whereas fairness in demand or surplus reduces social welfare. We fully characterize the impact of imposing different types of fairness for linear demand. We also discover that imposing too much price fairness may result in a lower social welfare relative to imposing no price fairness. Finally, we computationally show that most of our findings continue to hold for three common nonlinear demand models. Our results and insights provide a first step in understanding the impact of imposing fairness in the context of discriminatory pricing.
Better Together? How Externalities of Size Complicate Notions of Solidarity and Actuarial Fairness
Consider a cost-sharing game with players of different costs: an example might be an insurance company calculating premiums for a population of mixed-risk individuals. Two natural and competing notions of fairness might be to a) charge each individual the same or b) charge each individual according to the cost that they bring to the pool. In the insurance literature, these approaches are referred to as ""solidarity"" and ""actuarial fairness"" and are commonly viewed as opposites. However, in insurance (and many other natural settings), the cost-sharing game also exhibits ""externalities of size"": all else being equal, larger groups have lower average cost. In the insurance case, we analyze model where costs strictly decreases with pooling due to a reduction in the variability of losses. In this paper, we explore how this complicates traditional understandings of fairness, drawing on literature in cooperative game theory. First, we explore solidarity: we show that it is possible for both groups (high risk and low risk) to strictly benefit by joining an insurance pool where costs are evenly split, as opposed to being in separate risk pools. We build on this by producing a pricing scheme that maximally subsidizes the high risk group, while maintaining an incentive for lower risk people to stay in the insurance pool. Next, we demonstrate that with this new model, the price charged to each individual has to depend on the risk of other participants, making naive actuarial fairness inefficient. Furthermore, we prove that stable pricing schemes must be ones where players have the anti-social incentive desiring riskier partners, contradicting motivations for using actuarial fairness. Finally, we describe how these results relate to debates about fairness in machine learning and potential avenues for future research.
Fairness, Welfare, and Equity in Personalized Pricing
We study the interplay of fairness, welfare, and equity considerations in personalized pricing based on customer features. Sellers are increasingly able to conduct price personalization based on predictive modeling of demand conditional on covariates: setting customized interest rates, targeted discounts of consumer goods, and personalized subsidies of scarce resources with positive externalities like vaccines and bed nets. These different application areas may lead to different concerns around fairness, welfare, and equity on different objectives: price burdens on consumers, price envy, firm revenue, access to a good, equal access, and distributional consequences when the good in question further impacts downstream outcomes of interest. We conduct a comprehensive literature review in order to disentangle these different normative considerations and propose a taxonomy of different objectives with mathematical definitions. We focus on observational metrics that do not assume access to an underlying valuation distribution which is either unobserved due to binary feedback or ill-defined due to overriding behavioral concerns regarding interpreting revealed preferences. In the setting of personalized pricing for the provision of goods with positive benefits, we discuss how price optimization may provide unambiguous benefit by achieving a "triple bottom line": personalized pricing enables expanding access, which in turn may lead to gains in welfare due to heterogeneous utility, and improve revenue or budget utilization. We empirically demonstrate the potential benefits of personalized pricing in two settings: pricing subsidies for an elective vaccine, and the effects of personalized interest rates on downstream outcomes in microcredit.