Optimal combinatorial mechanism design

We consider an optimal mechanism design problem with several heterogenous objects and interdependent values. We characterize ex post incentives using an appropriate monotonicity condition and reformulate the problem in such a way that the choice of an allocation rule can be separated from the choice of the payment rule. Central to the analysis is the formulation of a regularity condition, which gives a recipe for the optimal mechanism. If the problem is regular, then an optimal mechanism can be obtained by solving a combinatorial allocation problem in which objects are allocated in a way to maximize the sum of virtual valuations. We identify conditions that imply regularity using the techniques of supermodular optimization.

[1]  Jerry J. Koliha,et al.  A Fundamental Theorem of Calculus for Lebesgue Integration , 2006, Am. Math. Mon..

[2]  Paul R. Milgrom,et al.  Monotone Comparative Statics , 1994 .

[3]  Vijay Krishna.  Asymmetric English auctions , 2003, J. Econ. Theory.

[4]  E. Maskin,et al.  Monopoly with Incomplete Information , 1984 .

[5]  E. Stacchetti,et al.  Multidimensional Mechanism Design for Auctions with Externalities , 1999 .

[6]  P. Monteiro.  Optimal auctions in a general model of identical goods , 2002 .

[7]  An E¢cient Auction ¤ , 2001 .

[8]  F. Hahn,et al.  Optimal Multi-Unit Auctions , 1989 .

[9]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[10]  D. M. Topkis.  Supermodularity and Complementarity , 1998 .

[11]  Thomas R. Palfrey,et al.  Bundling Decisions by a Multiproduct Monopolist with Incomplete Information , 1983 .

[12]  Lawrence M. Ausubel.  A Generalized Vickrey Auction , 2000 .

[13]  Yoav Shoham,et al.  Combinatorial Auctions , 2005, Encyclopedia of Wireless Networks.

[14]  John O. Ledyard,et al.  Optimal combinatoric auctions with single-minded bidders , 2007, EC '07.

[15]  Daniel Lehmann,et al.  Combinatorial auctions with decreasing marginal utilities , 2001, EC '01.

[16]  Moshe Tennenholtz,et al.  Bundling equilibrium in combinatorial auctions , 2002, Games Econ. Behav..

[17]  Dilip Mookherjee,et al.  Dominant Strategy Implementation of Bayesian incentive Compatible Allocation Rules , 1992 .

[18]  F. Hahn.  The Economics of missing markets, information, and games , 1990 .

[19]  Lawrence M. Ausubel,et al.  The Optimality of Being Efficient , 1999 .

[20]  Richard P. McLean,et al.  Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent , 1985 .

[21]  Paul R. Milgrom,et al.  Envelope Theorems for Arbitrary Choice Sets , 2002 .

[22]  P. Cramton,et al.  Introduction to Combinatorial Auctions , 2006 .

[23]  J. Rochet.  A necessary and sufficient condition for rationalizability in a quasi-linear context , 1987 .

[24]  Lawerence M. Cramton Peter Ausubel.  The optimality of being efficient: designing auctions , 1998 .

[25]  P. Reny,et al.  AN EFFICIENT AUCTION , 2002 .

[26]  N. Kukushkin.  Monotone comparative statics: changes in preferences versus changes in the feasible set , 2013 .

[27]  Fernando Branco,et al.  Multiple unit auctions of an indivisible good , 1996 .

[28]  V. Krishna,et al.  Convex Potentials with an Application to Mechanism Design , 2001 .

[29]  Jonathan D. Levin.  An Optimal Auction for Complements , 1997 .

[30]  Cristina Mazón,et al.  Multi-unit auctions with private information: an indivisible unit continuous price model , 2012 .