We consider the problem of designing auctions which maximize consumer surplus (i.e., the social welfare minus the payments charged to the buyers). In the consumer surplus maximization problem, a seller with a set of goods faces a set of strategic buyers with private values, each of whom aims to maximize their own individual utility. The seller, in contrast, aims to allocate the goods in a way which maximizes the total buyer utility. The seller must then elicit the values of the buyers in order to decide what goods to award each buyer. The canonical approach in mechanism design to ensure truthful reporting of the private information is to find appropriate prices to charge each buyer in order to align their objective with the objective of the seller. Indeed, there are many celebrated results to this end when the seller's objective is welfare maximization [Clarke, 1971, Groves, 1973, Vickrey, 1961] or revenue maximization [Myerson, 1981]. However, in the case of consumer surplus maximization the picture is less clear -- using high payments to ensure the highest value bidders are served necessarily decreases their surplus utility, but using low payments may lead the seller into serving lower value bidders. Our main result in this paper is a framework for designing mechanisms which maximize consumer surplus. We instantiate our framework in a variety of canonical multi-parameter auction settings (i.e., unit-demand bidders with heterogeneous items, multi-unit auctions, and auctions with divisible goods) and use it to design auctions achieving consumer surplus with optimal approximation guarantees against the total social welfare. Along the way, we answer an open question posed by Hartline and Roughgarden [2008], who, to our knowledge, were the first to study the question of consumer surplus approximation guarantees in single-parameter settings, regarding optimal mechanisms for two bidders.

翻译：我们研究旨在最大化消费者剩余（即社会总福利减去向买家收取的支付额）的拍卖设计问题。在消费者剩余最大化问题中，拥有商品组合的卖方面对一组具有私有价值的策略性买家，每位买家都力图最大化自身个体效用。与之相对，卖方则倾向于以最大化买家总效用的方式分配商品。为决定向每位买家授予何种商品，卖方必须诱导买家的真实价值披露。机制设计中确保私有信息真实报告的标准方法，是设定合适的买家定价以使其目标与卖方目标一致。确实，当卖方目标为福利最大化[Clarke, 1971, Groves, 1973, Vickrey, 1961]或收益最大化[Myerson, 1981]时，已有诸多著名结论。然而在消费者剩余最大化情形下，图景却更为模糊——通过高额支付确保最高价值买家获得服务必然降低其剩余效用，但低额支付又可能使卖方服务于低价值买家。本文的主要贡献是构建了最大化消费者剩余的机制设计框架。我们在多种经典多参数拍卖场景（包括异质商品下的单位需求买家、多单元拍卖及可分割商品拍卖）中实例化该框架，并据此设计出在最优近似比下（相对于总社会福利）实现消费者剩余的拍卖机制。在此过程中，我们解答了Hartline与Roughgarden[2008]提出的开放性问题——据我们所知，他们首次研究了单参数环境下消费者剩余近似保证问题，其中涉及双买家情形下的最优机制。