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Matching Models for Preference-sensitive Group Purchasing

Matching 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

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 valuations—a model that is especially

attractive in the consumer space—which 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.4

[Computer Applications]: Social and Behavioral Sciences—Economics

General Terms: Algorithms, Economics, Theory

Additional Key Words and Phrases: stable matching, preferences, demand aggregation, group

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

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

demand[Anand 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 with volume discounts assume that vendor offerings are

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.While matching becomes

much more subtle in such models, assigning buyers to vendors in a way that triggers volume

discounts, while remaining sensitive to buyer preferences, offers flexibility and efficiency gains

that greatly enhance the appeal of group buying. Consider a group of businesses or buyers

working with a GPO to procure supplies within a specific product category (e.g., manufacturing

materials, packaging, transportation, payroll services, etc.). The GPO is able to negotiate volume

Suppose a daily deal aggregator creates a “marketplace” for some product category, say, spas.

Multiple spas offer deals that only trigger if a certain quantity is sold. Buyers are faced with a

if their preferred deal does not trigger. But if they offer on multiple spas to hedge that risk, they

run the opposite risk of obtaining more items than they want. A matching model that allows

consumers to specify preferences for items relative to their discounted prices provides flexibility

vendors offering products (e.g., within a specific product category). Interacting with some GPO or

informal buying group, vendors offer (possibly multiple) volume discounts that trigger if the