zbMATH — the first resource for mathematics

Multidimensional mechanism design for auctions with externalities. (English) Zbl 1028.91539
Summary: In an auction with externalities, a buyer’s type is multidimensional and specifies the payoff he would get for each of the \(N+ 1\) possible outcomes: the seller keeps the object or buyer \(i\) \((i= 1,\dots, N)\) gets the object. We provide a characterization of multidimensional incentive compatible mechanisms similar to that for one-dimensional mechanisms. Although reservation utilities are endogenous and type-dependent, the participation constraint is binding for only one “critical” type. A main difficulty in a multidimensional setting is the “integrability” condition. We present a geometric characterization for discontinuous conservative vector fields. In auctions where the buyers submit scalar bids and the seller transfers the object to one of the buyers for sure, a second-price auction maximizes revenue. With two buyers, this auction remains optimal even if the seller can set a reservation price.

91B26 Auctions, bargaining, bidding and selling, and other market models
Full Text: DOI
[1] Armstrong, M., Multiproduct nonlinear pricing, Econometrica, 64, 51-75, (1996) · Zbl 0861.90015
[2] Champsaur, P.; Rochet, J. C., Multiproduct duopolists, Econometrica, 57, 533-588, (1989) · Zbl 0692.90010
[3] Jehiel, P.; Moldovanu, B.; Stacchetti, E., How (not) to Sell nuclear weapons, Amer. Econ. Rev., 86, 814-829, (1996)
[4] V. Krishna, E. Maenner, A path independence result for convex functions with an application to mechanism design, Penn State University, 1998
[5] Laffont, J. J.; Maskin, E.; Rochet, J. C., Optimal nonlinear pricing with two-dimensional characteristics, Information, Incentives, and Economic Mechanisms, (1987), University of Minnesota Press Minneapolis, p. 256-266
[6] Laffont, J. J.; Tirole, J., The regulation of multiproduct firms, part I: theory, J. Public Econ., 43, 1-36, (1990)
[7] Lewis, T.; Sappington, D., Regulating a monopolist with unknown demand and cost functions, Rand J. Econ., 19, 438-457, (1988)
[8] Matthews, S.; Moore, J., Monopoly provision of quality and warranties: an exploration in the theory of multidimensional screening, Econometrica, 55, 441-468, (1987) · Zbl 0609.90009
[9] McAfee, R. P.; McMillan, J., Multidimensional incentive compatibility and mechanism design, J. Econ. Theory, 46, 335-354, (1988) · Zbl 0661.90008
[10] McAfee, R. P.; McMillan, J.; Whinson, M. D., Multiproduct monopoly, commodity bundling, and correlation of values, Quart. J. Econ., 93, 371-383, (1989)
[11] Milgrom, P.; Weber, R., A theory of auctions and competitive bidding, Econometrica, 50, 1089-1122, (1982) · Zbl 0487.90017
[12] Mirman, L. J.; Sibley, D., Optimal nonlinear prices for multiproduct monopolies, Bell. J. Econ., 11, 659-670, (1980)
[13] Myerson, R., Optimal auction design, Math. Oper. Res., 6, 58-63, (1981) · Zbl 0496.90099
[14] Palfrey, T. R., Bundling decisions by a multiproduct monopolist with incomplete information, Econometrica, 51, 463-483, (1983) · Zbl 0495.90014
[15] Rochet, J. C., The taxation principle and multitime hamilton – jacobi equations, J. Math. Econ., 14, 93-128, (1985) · Zbl 0594.90006
[16] Rochet, J. C.; ChonĂ©, P., Ironing, sweeping and multidimensional screening, Econometrica, 66, 783-826, (1998) · Zbl 1015.91515
[17] Rockafellar, R. T., Convex Analysis, (1972), Princeton University Press Princeton · Zbl 0224.49003
[18] Rockafellar, R. T., Conjugate Duality and Optimization, (1974), SIAM Philadelphia · Zbl 0326.49008
[19] Spence, A. M., Multi-product quantity-dependent prices and profitability constraints, Rev. Econ. Stud., 47, 821-841, (1980) · Zbl 0444.90016
[20] Wilson, R., Multiproduct tariffs, J. Regulatory Econ., 3, 5-26, (1991)
[21] Wilson, R., Nonlinear Pricing, (1993), Oxford Univ. Press Oxford
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.