Efficient Constrained Combinatorial Auctions

Anat Lerner () and Rica Gonen ()
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Rica Gonen: Department of Management and Economics, The Open University of Israel, 1 University Road, Raanana 4353701, Israel

International Game Theory Review (IGTR), 2016, vol. 18, issue 03, 1-10

Abstract: The seminal work by Green and Laffont [(1977) characterization of satisfactory mechanisms for the revelation of preferences for public goods, Econometrica 45, 427–438] shows that efficient mechanisms with Vickrey–Clarke–Groves prices satisfy the properties of dominant-strategy incentive compatible (DSIC) and individually rational in the quasilinear utilities model. Nevertheless in many real-world situations some players have a gap between their willingness to pay and their ability to pay, i.e., a budget. We show that once budgets are integrated into the model then Green and Laffont’s theorem ceases to apply. More specifically, we show that even if only a single player has budget constraints then there is no deterministic efficient mechanism that satisfies the individual rationality and DSIC properties. Furthermore, in a quasilinear utilities model with k nonidentical items and n players with multidimensional types, we characterize the sufficient and necessary conditions under which Green and Laffont’s theorem holds in the presence of budget-constrained players. Interestingly our characterization is similar in spirit to that of Maskin [(2000) Auctions, development and privatization: Efficient auctions with liquidity-constrained buyers, Eur. Econ. Rev. 44, 667–681] for Bayesian single-item constrained-efficiency auctions.

Keywords: Budget constraints; efficiency; incentive compatibility (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0219198916500079

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