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Games 2014, 5(2), 97-115; doi:10.3390/g5020097
Article

Characterizing the Incentive Compatible and Pareto Optimal Efficiency Space for Two Players, k Items, Public Budget and Quasilinear Utilities

1
 and
2,*
1 Department of Mathematics and Computer Science, The Open University of Israel, 1 University Road, Raanana 4353701, Israel 2 Department of Management and Economics, The Open University of Israel, 1 University Road, Raanana 4353701, Israel
* Author to whom correspondence should be addressed.
Received: 9 December 2013 / Revised: 1 April 2014 / Accepted: 17 April 2014 / Published: 30 April 2014
Download PDF [239 KB, 7 May 2014; original version 30 April 2014]

Abstract

We characterize the efficiency space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto-optimal combinatorial auctions in a model with two players and k nonidentical items. We examine a model with multidimensional types, private values and quasilinear preferences for the players with one relaxation: one of the players is subject to a publicly known budget constraint. We show that if it is publicly known that the valuation for the largest bundle is less than the budget for at least one of the players, then Vickrey-Clarke-Groves (VCG) uniquely fulfills the basic properties of being deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal. Our characterization of the efficient space for deterministic budget constrained combinatorial auctions is similar in spirit to that of Maskin 2000 for Bayesian single-item constrained efficiency auctions and comparable with Ausubel and Milgrom 2002 for non-constrained combinatorial auctions.
Keywords: budget constraints; Pareto efficiency; incentive compatibility budget constraints; Pareto efficiency; incentive compatibility
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Lerner, A.; Gonen, R. Characterizing the Incentive Compatible and Pareto Optimal Efficiency Space for Two Players, k Items, Public Budget and Quasilinear Utilities. Games 2014, 5, 97-115.

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