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Characterizing the Efficiency of Static Pricing Schemes as a Function of the Supply The problem of selling a supply of k units to a stream of customers constitutes one of the cornerstones in revenue management. Static pricing schemes (that output the same price to all customers) are commonly used because of their simplicity and their many desirable properties; they are anonymous, nonadaptive, and order oblivious. Although the efficiency of those schemes should improve as the supply k increases, prior work has only focused either on algorithms that aim for a constant approximation that is independent of k or on the setting where k becomes really large. In contrast, this paper characterizes the efficiency of static pricing schemes as a function of the supply. Our approach stems from identifying a “sweet spot” between selling enough items and obtaining enough utility from customers with high valuations. Subsequent work shows that our pricing scheme is the optimal static pricing for every value of k. 

We study methods for improving fairness to subgroups in settings with overlapping populations and sequential predictions. Classical notions of fairness focus on the balance of some property across different populations. However, in many applications the goal of the different groups is not to be predicted equally but rather to be predicted well. We demonstrate that the task of satisfying this guarantee for multiple overlapping groups is not straightforward and show that for the simple objective of unweighted average of false negative and false positive rate, satisfying this for overlapping populations can be statistically impossible even when we are provided predictors that perform well separately on each subgroup. On the positive side, we show that when individuals are equally important to the different groups they belong to, this goal is achievable; to do so, we draw a connection to the sleeping experts literature in online learning. Motivated by the one-sided feedback in natural settings of interest, we extend our results to such a feedback model. We also provide a game-theoretic interpretation of our results, examining the incentives of participants to join the system and to provide the system full information about predictors they may possess. We end with several interesting open problems concerning the strength of guarantees that can be achieved in a computationally efficient manner.