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Modeling profit sharing in combinatorial exchanges by network flows

  • In this paper we study the possibilities of sharing profit in combinatorial procurement auctions and exchanges. Bundles of heterogeneous items are offered by the sellers, and the buyers can then place bundle bids on sets of these items. That way, both sellers and buyers can express synergies between items and avoid the well-known risk of exposure (see, e.g., [3]). The reassignment of items to participants is known as the Winner Determination Problem (WDP). We propose solving the WDP by using a Set Covering formulation, because profits are potentially higher than with the usual Set Partitioning formulation, and subsidies are unnecessary. The achieved benefit is then to be distributed amongst the participants of the auction, a process which is known as profit sharing. The literature on profit sharing provides various desirable criteria. We focus on three main properties we would like to guarantee: Budget balance, meaning that no more money is distributed than profit was generated, individual rationality, which guarantees to each player that participation does not lead to a loss, and the core property, which provides every subcoalition with enough money to keep them from separating. We characterize all profit sharing schemes that satisfy these three conditions by a monetary flow network and state necessary conditions on the solution of the WDP for the existence of such a profit sharing. Finally, we establish a connection to the famous VCG payment scheme [2, 8, 19], and the Shapley Value [17].

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Author:H. Ackermann, H. Ewe, K.-H. Küfer, M. Schröder
URN (permanent link):urn:nbn:de:hbz:386-kluedo-16964
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (205)
Document Type:Report
Language of publication:English
Year of Completion:2011
Year of Publication:2011
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2011/05/04
Tag:Shapley Value; VCG payment scheme; Winner Determination Problem (WDP); combinatorial procurement
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011