Robust Revenue Maximization Under Minimal Statistical Information

We study the problem of multi-dimensional revenue maximization when selling $m$ items to a buyer that has additive valuations for them, drawn from a (possibly correlated) prior distribution. Unlike traditional Bayesian auction design, we assume that the seller has a very restricted knowledge of this prior: they only know the mean $\mu_j$ and an upper bound $\sigma_j$ on the standard deviation of each item's marginal distribution. Our goal is to design mechanisms that achieve good revenue against an ideal optimal auction that has full knowledge of the distribution in advance. Informally, our main contribution is a tight quantification of the interplay between the dispersity of the priors and the aforementioned robust approximation ratio. Furthermore, this can be achieved by very simple selling mechanisms. More precisely, we show that selling the items via separate price lotteries achieves an $O(\log r)$ approximation ratio where $r=\max_j(\sigma_j/\mu_j)$ is the maximum coefficient of variation across the items. If forced to restrict ourselves to deterministic mechanisms, this guarantee degrades to $O(r^2)$. Assuming independence of the item valuations, these ratios can be further improved by pricing the full bundle. For the case of identical means and variances, in particular, we get a guarantee of $O(\log(r/m))$ which converges to optimality as the number of items grows large. We demonstrate the optimality of the above mechanisms by providing matching lower bounds. Our tight analysis for the deterministic case resolves an open gap from the work of Azar and Micali [ITCS'13]. As a by-product, we also show how one can directly use our upper bounds to improve and extend previous results related to the parametric auctions of Azar et al. [SODA'13]

Profit Efficiency Analysis Under Limited Information. With an Application to German Farm Types

Lack of information about technology and prices often hampers the empirical assessment of the validity of the profit maximization hypothesis. We show that the non-parametric Data Envelopment Analysis (DEA) methodology comprises natural tools for dealing with such incomplete information. In particular, we focus on the economic meaning of the DEA model that builds on assumptions of monotone and convex production possibility sets, and provide some extensions that further exploit this economic interpretation. This perspective on DEA is all the more attractive since its original use for technical efficiency analysis is sometimes questionable given its restrictive production assumptions. An application to German farm types complements our methodological discussion. By using nonparametric tools to test specific hypotheses about profit differences, we further demonstrate the potential of the non-parametric approach in deriving strong and robust statistical evidence while imposing minimal structure on the setting under study.profit maximization hypothesis; Data Envelopment Analysis; non-parametric techniques; agriculture

Profit efficiency analysis under limited information. With an application to German farm types.

Efficiency; Information;

Protecting the Protected Group: Circumventing Harmful Fairness

Machine Learning (ML) algorithms shape our lives. Banks use them to determine if we are good borrowers; IT companies delegate them recruitment decisions; police apply ML for crime-prediction, and judges base their verdicts on ML. However, real-world examples show that such automated decisions tend to discriminate against protected groups. This potential discrimination generated a huge hype both in media and in the research community. Quite a few formal notions of fairness were proposed, which take a form of constraints a "fair" algorithm must satisfy. We focus on scenarios where fairness is imposed on a self-interested party (e.g., a bank that maximizes its revenue). We find that the disadvantaged protected group can be worse off after imposing a fairness constraint. We introduce a family of \textit{Welfare-Equalizing} fairness constraints that equalize per-capita welfare of protected groups, and include \textit{Demographic Parity} and \textit{Equal Opportunity} as particular cases. In this family, we characterize conditions under which the fairness constraint helps the disadvantaged group. We also characterize the structure of the optimal \textit{Welfare-Equalizing} classifier for the self-interested party, and provide an algorithm to compute it. Overall, our \textit{Welfare-Equalizing} fairness approach provides a unified framework for discussing fairness in classification in the presence of a self-interested party.Comment: Published in AAAI 202

Free Ride, Take it Easy: An Empirical Analysis of Adverse Incentives Caused by Revenue Sharing

A fundamental belief in professional sport leagues is that competitive balance is needed to maximize demand and revenues; therefore, leagues have created policies attempting to attain proper competitive balance. Further, research posits that objectives of professional sport teams’ owners include some combination of winning and profit maximization. Although the pursuit of wins is a zero sum game, revenue generation and potential profit making is not. This article focuses upon the National Football League’s potential unintended consequences of creating the incentive for some teams to free ride on the rest of the league’s talent and brand. It examines whether an owner’s objectives to generate increased revenues and profits are potentially enhanced by operating as a continual low-cost provider while making money from the shared revenues and brand value of the league. The present evidence indicates that, overall, being a low-cost provider is more profitable than increasing player salaries in an attempt to win additional games.free riding; free ride; football; profit maximization; regression; owner incentives