We study large markets with a single seller which can produce many types of goods, and many multi-minded buyers. The seller chooses posted prices for its many items, and the buyers purchase bundles to maximize their utility. For this setting, we consider the following questions: What fraction of the optimum social welfare does a revenue maximizing solution achieve? Are there pricing mechanisms which achieve both good revenue and good welfare simultaneously? To address these questions, we give efficient pricing schemes which are guaranteed to result in both good revenue and welfare, as long as the buyer valuations for the goods they desire have a nice (although reasonable) structure, e.g., that the aggregate buyer demand has a monotone hazard rate or is not too convex. We also show that our pricing schemes have implications for any pricing which achieves high revenue: specifically that even if the seller cares only about revenue, they can still ensure that their prices result in good social welfare without sacrificing profit. Our results holds for general multi-minded buyers in large markets; we also provide improved guarantees for the important special case of unit-demand buyers.
In this paper, we provide a transform from an $\varepsilon$-BIC mechanism into an exactly BIC mechanism without any loss of social welfare and with additive and negligible revenue loss. This is the first $\varepsilon$-BIC to BIC transformation that preserves welfare and provides negligible revenue loss. The revenue loss bound is tight given the requirement to maintain social welfare. Previous $\varepsilon$-BIC to BIC transformations preserve social welfare but have no revenue guarantee~\citep{BeiHuang11}, or suffer welfare loss while incurring a revenue loss with both a multiplicative and an a…
This paper considers Bayesian revenue maximization in the $k$-unit setting, where a monopolist seller has $k$ copies of an indivisible item and faces $n$ unit-demand buyers (whose value distributions can be non-identical). Four basic mechanisms among others have been widely employed in practice and widely studied in the literature: {\sf Myerson Auction}, {\sf Sequential Posted-Pricing}, {\sf $(k + 1)$-th Price Auction with Anonymous Reserve}, and {\sf Anonymous Pricing}. Regarding a pair of mechanisms, we investigate the largest possible ratio between the two revenues (a.k.a.\ the revenue gap)…
The common way to optimize auction and pricing systems is to set aside a small fraction of the traffic to run experiments. This leads to the question: how can we learn the most with the smallest amount of data? For truthful auctions, this is the \emph{sample complexity} problem. For posted price auctions, we no longer have access to samples. Instead, the algorithm is allowed to choose a price $p_t$; then for a fresh sample $v_t \sim \mathcal{D}$ we learn the sign $s_t = sign(p_t - v_t) \in \{-1,+1\}$. How many pricing queries are needed to estimate a given parameter of the underlying distribut…
We study fairness in the context of feature-based price discrimination in monopoly markets. We propose a new notion of individual fairness, namely, α-fairness, which guarantees that individuals with similar features face similar prices. First, we study discrete valuation space and give an analytical solution for optimal fair feature-based pricing. We show that the cost of fair pricing is defined as the ratio of expected revenue in an optimal feature-based pricing to the expected revenue in an optimal fair feature-based pricing (CoF) can be arbitrarily large in general. When the revenue functio…
A major challenge for ridesharing platforms is to guarantee profit and fairness simultaneously, especially in the presence of misaligned incentives of drivers and riders. We focus on the dispatching-pricing problem to maximize the total revenue while keeping both drivers and riders satisfied. We study the computational complexity of the problem, provide a novel two-phased pricing solution with revenue and fairness guarantees, extend it to stochastic settings and develop a dynamic (a.k.a., learning-while-doing) algorithm that actively collects data to learn the demand distribution during the sc…
We study market mechanisms for allocating divisible goods to competing agents with quasilinear utilities. For \emph{linear} pricing (i.e., the cost of a good is proportional to the quantity purchased), the First Welfare Theorem states that Walrasian equilibria maximize the sum of agent valuations. This ensures efficiency, but can lead to extreme inequality across individuals. Many real-world markets -- especially for water -- use \emph{convex} pricing instead, often known as increasing block tariffs (IBTs). IBTs are thought to promote equality, but there is a dearth of theoretical support for …
In this paper, we introduce a Bayesian revenue-maximizing mechanism design model where the items have fixed, exogenously-given prices. Buyers are unit-demand and have an ordinal ranking over purchasing either one of these items at its given price, or purchasing nothing. This model arises naturally from the assortment optimization problem, in that the single-buyer optimization problem over deterministic mechanisms reduces to deciding on an assortment of items to "show". We study its multi-buyer generalization in the simplest setting of single-winner auctions, or more broadly, any service-constr…
We consider a fundamental problem in microeconomics: selling a single item to a number of potential buyers, whose values are drawn from known independent and regular (not necessarily identical) distributions. There are four widely-used and widely-studied mechanisms in the literature: { \sf Myerson Auction}~({ \sf OPT}), { \sf Sequential Posted-Pricing}~({ \sf SPM}), { \sf Second-Price Auction with Anonymous Reserve}~({ \sf AR}), and { \sf Anonymous Pricing}~({ \sf AP}). { \sf OPT} is revenue-optimal but complicated, which also experiences several issues in practice such as fairness; { \sf AP} …
A ubiquitous learning problem in today's digital market is, during repeated interactions between a seller and a buyer, how a seller can gradually learn optimal pricing decisions based on the buyer's past purchase responses. A fundamental challenge of learning in such a strategic setup is that the buyer will naturally have incentives to manipulate his responses in order to induce more favorable learning outcomes for him. To understand the limits of the seller's learning when facing such a strategic and possibly manipulative buyer, we study a natural yet powerful buyer manipulation strategy. Tha…
A patient seller aims to sell a good to an impatient buyer (i.e., one who discounts utility over time). The buyer will remain in the market for a period of time $T$, and her private value is drawn from a publicly known distribution. What is the revenue-optimal pricing-curve (sequence of (price, time) pairs) for the seller? Is randomization of help here? Is the revenue-optimal pricing curve computable in polynomial time? We answer these questions in this paper. We give an efficient algorithm for computing the revenue-optimal pricing curve. We show that pricing curves, that post a price at each …
We consider the problem of posting prices for unit-demand buyers if all $n$ buyers have identically distributed valuations drawn from a distribution with monotone hazard rate. We show that even with multiple items asymptotically optimal welfare can be guaranteed. Our main results apply to the case that either a buyer's value for different items are independent or that they are perfectly correlated. We give mechanisms using dynamic prices that obtain a $1 - Θ\left( \frac{1}{\log n}\right)$-fraction of the optimal social welfare in expectation. Furthermore, we devise mechanisms that only use sta…
We study the revenue guarantees and approximability of item pricing. Recent work shows that with $n$ heterogeneous items, item-pricing guarantees an $O(\log n)$ approximation to the optimal revenue achievable by any (buy-many) mechanism, even when buyers have arbitrarily combinatorial valuations. However, finding good item prices is challenging -- it is known that even under unit-demand valuations, it is NP-hard to find item prices that approximate the revenue of the optimal item pricing better than $O(\sqrt{n})$. Our work provides a more fine-grained analysis of the revenue guarantees and com…
Online markets are a part of everyday life, and their rules are governed by algorithms. Assuming participants are inherently self-interested, well designed rules can help to increase social welfare. Many algorithms for online markets are based on prices: the seller is responsible for posting prices while buyers make purchases which are most profitable given the posted prices. To make adjustments to the market the seller is allowed to update prices at certain timepoints. Posted prices are an intuitive way to design a market. Despite the fact that each buyer acts selfishly, the seller's goal is …
Standard ad auction formats do not immediately extend to settings where multiple size configurations and layouts are available to advertisers. In these settings, the sale of web advertising space increasingly resembles a combinatorial auction with complementarities, where truthful auctions such as the Vickrey-Clarke-Groves (VCG) can yield unacceptably low revenue. We therefore study core selecting auctions, which boost revenue by setting payments so that no group of agents, including the auctioneer, can jointly improve their utilities by switching to a different outcome. Our main result is a c…
我们认为优先级自由拍卖收入和福利最大化时，代理人有一个共同的预算。我们考虑的抽象环境是有一个向下封闭的和对称的可行性约束的代理服务的概率。这些环境包括位置拍卖，其中具有降低的点击率的位置被拍卖给广告商。我们将Hartline和Yan（2011）的无嫉妒基准推广和表征到有预算的环境中，并表征福利和收入的最佳无嫉妒结果。我们给出了近似这些基准的无先验机制。在我们的机制的一个组成部分是一个成交拍卖的位置拍卖环境。该拍卖是Dobzinski et al.（2008）的多单位成交拍卖的推广，也是Goel et al.（2012）的多面体成交拍卖的特例。对于福利最大化，我们表明，这种成交拍卖是一个很好的近似的嫉妒无最优福利的位置拍卖环境。对于利润最大化，我们推广了Fiat等人（2002）的随机抽样利润提取拍卖，用于数字商品，以给出对称下闭环境中无嫉妒最优收入的10.0近似值。即使没有预算，利润最大化问题也很有趣，我们的机制是一个7.5近似，改进了Ha和Hartline（2012）的30.4界限。
We study the worst-case welfare of item pricing in the \emph{tollbooth problem}. The problem was first introduced by Guruswami et al, and is a special case of the combinatorial auction in which (i) each of the $m$ items in the auction is an edge of some underlying graph; and (ii) each of the $n$ buyers is single-minded and only interested in buying all edges of a single path. We consider the competitive ratio between the hindsight optimal welfare and the optimal worst-case welfare among all item-pricing mechanisms, when the order of the arriving buyers is adversarial. We assume that buyers own…
