外文翻译原文1Matching Models for Preference-sensitive Group PurchasingMatching buyers and sellers is one of the most fundamental problems in economics and market design. An interesting variant of the matching problem arises when self-interested buyers come together in order to induce sellers to offer quantity or volume discounts, as is common in buying consortia, and more recently in the consumer group couponing space (e.g., Groupon).We consider a general model of this problem in which a group or buying consortium is faced with volume discount offers from multiple vendors, but group members have distinct preferences for different vendor offerings. Unlike some recent formulations of matching games that involve quantity discounts, the combination of varying preferences and discounts can render the core of the matching game empty, in both the transferable and nontransferable utility sense. Thus, instead of coalitional stability, we propose several forms of Nash stability under various epistemic and transfer/payment assumptions. We investigate the computation of buyer-welfare maximizing matchings and show the existence of transfers (subsidized prices) of a particularly desirable form that support stable matchings. We also study a nontransferable utility model, showing that stable matchings exist; and we develop a variant of the problem in which buyers provide a simple preference ordering over “deals” rather than specific valuationsa model that is especially attractive in the consumer spacewhich also admits stable matchings. Computational experiments demonstrate the efficacy and value of our approach. Categories and Subject Descriptors: I.2.11 Distributed Artificial Intelligence: Multiagent Systems; J.4Computer Applications: Social and Behavioral SciencesEconomicsGeneral Terms: Algorithms, Economics, TheoryAdditional Key Words and Phrases: stable matching, preferences, demand aggregation, group purchasing,volume discounts, daily deals, cooperative games.1. INTRODUCTIONMatching buyers and sellers is one of the most fundamental problems in economics anddeal” providers like Groupon and Living Social (and services that aggregate such deals) has propelled group discounts into the public consciousness.Group buying and demand aggregation has been studied from several perspectives, and many models have been proposed for their analysis. However, we consider a vital ingredient of group buying that has received insufficient attention in the literature, namely, the fact that buyers often have distinct preferences for the offerings of different vendors. Most matching models with volume discounts assume that vendor offerings are indistinguishable to buyers, which significantly limits their applicability. For instance,suppose two buyers X and Y are (jointly) comparing the offers of two vendors or some item: A offers a price of 10 for one unit, but a discounted price of 8 if both buy from him; and B offers a single price of 9 per unit. If A and B are indistinguishable, X and Y should cooperate and buy from A. But suppose X prefers B (with valuation 11.5) to A (valuation 10). In this case, X would prefer to stick with B unless Y offers some payment to switch vendors (Y would gladly share some of her generated surplus with X for this purpose). Without the ability to express preferences over vendors, “group buying” would not emerge even in this trivial example. market design. A wide variety of models and mechanisms have been developed that reflect different assumptions about the demands, valuations/preferences, and knowledge of the market participants and their ability to cooperate. Each leads to its own computational challenges when developing algorithms for computing stable (core) matchings,Nash equilibria, clearing prices or other solution concepts. In this paper, we address the problem of cooperative group buying, in which a group of buyers coordinate their purchases to realize volume discounts, mitigate demand risk, or reduce inventory costs. Group buying has long been used for corporate procurement,via industry-specific buying consortia or broadly based group purchasingorganizations (GPOs) Chen and Roma 2010. The advent of the Internet, in particular,has helped businesses with no prior affiliation more easily aggregate their demandAnand and Aron 2003. Consumer-oriented group purchasing has also been greatly facilitatedby the web; and the recent popularity of volume-based couponing and “dailydeal” providers like Groupon and Living Social (and services that aggregate such deals)has propelled group discounts into the public consciousness.Group buying and demand aggregation has been studied from several perspectives,and many models have been proposed for their analysis. However, we consider a vital ingredient of group buying that has received insufficient attention in the literature,namely, the fact that buyers often have distinct preferences for the offerings of different vendors. Most matching models wit