Combinatorial Auctions: A Survey

Abstract

Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes and furniture. Because of complementarities (or substitution effects) between the different assets, bidders have preferences not just for particular items but for sets or bundles of items. For this reason, economic efficiency is enhanced if bidders are allowed to bid on bundles or combinations of different assets. This paper surveys the state of knowledge about the design of combinatorial auctions. Second, it uses this subject as a vehicle to convey the aspects of integer programming that are relevant for the design of such auctions and combinatorial markets in general.

GRASP with Hybrid Path Relinking for Bi-Objective Winner Determination in Combinatorial Transportation Auctions

“…There exists a multitude of WDP models for different scenarios (for an overview, see, e.g., De Vries andVohra 2003 or Abrache, Crainic, andRekik 2007). However, multi-objective formulations of the winner determination problem are still missing.…”

Managing Online Auctions: Current Business and Research Issues

“…Auctions in which bidders are interested in different, possibly overlapping, bundles of goods require new mechanisms for determining prices and allocating goods to bidders. The design of these so-called combinatorial auctions has attracted much interest in the academic community (see DeVries andVohra 2001, Rothkopf et al 1998). Finally, computational advances are improving the multimedia capabilities of the Internet, improving the ability to describe more complex products and further expanding the scope of products that can be auctioned.…”

Auctions, Bidding and Exchange Design

“…There are special cases under which the structure of this problem simplifies and allows for polynomial time solutions. Many special cases arise out of constraints that reduce the constraint matrix to be totally unimodular [dVV02]. A common example is the case where adjacent plots of land are being sold and bidders might want multiple plots but they need to be adjacent.…”

“…For example, the winner-determination problem in the VCG mechanism for a combinatorial auction can be solved in polynomial time with particular assumptions about the structure of agent valuations [RPH98,dVV02]. A number of fast algorithms have also been developed to solve the winner-determination problem in combinatorial auctions, even though the problem remains theoretically intractable [SSGL01a, FLBS99, ATY00].…”