Mmf fls afa sflassflassf ffffffffffffffffffffffffffffffffffff Discussion Papers Dynamic Marginal Contribution Mechanism Dirk Bergemann Yale University and Juuso V lim ki Helsinki School of Economics University of Southampton CEPR and HECER Discussion Paper No 176 July 2007 ISSN 1795 0562 HECER Helsinki Center of Economic Research P O Box 17 Arkadiankatu 7 FI 00014 University of Helsinki FINLAND Tel 358 9 191 28780 Fax 358 9 191 28781 E mail info hecer helsinki fi Internet www hecer fi HECER Discussion Paper No 176 Dynamic Marginal Contribution Mechanism Abstract We consider truthful implementation of the socially efficient allocation in a dynamic private value environment in which agents receive private information over time We propose a suitable generalization of the Vickrey Clarke Groves mechanism based on the marginal contribution of each agent In the marginal contribution mechanism the ex post incentive and ex post participations constraints are satisfied for all agents after all histories It is the unique mechanism satisfying ex post incentive ex post participation and efficient exit conditions We develop the marginal contribution mechanism in detail for a sequential auction of a single object in which only the current winner receives additional information about the object We show that a modified second price auction leads to truthtelling JEL Classification C72 C73 D43 D83 Keywords Vickrey Clarke Groves Mechanism Pivotal Mechanism Ex Post Equilibrium Marginal Contribution Dynamic Allocation Index Multi Armed Bandit Bayesian Learning Dirk Bergemann Juuso V lim ki Department of Economics Yale University New Haven CT 06520 8268 U S A Department of Economics Helsinki School of Economics P O Box 1210 Arkadiankatu 7 FI 00100 Helsinki FINLAND e mail dirk bergemann econ yale edu e mail valimaki hse fi We wish to thank the editor Eddie Dekel and three anonymous referees for many helpful comments The current paper is a major revision and supersedes Efficient Dynamic Auctions 2006 We are grateful to Larry Ausubel Jerry Green Paul Healy John Ledyard Michael Ostrovsky and David Parkes for many informative conversations The authors gratefully acknolwedge financial support through the National Science Foundation Grants CNS 0428422 and SES 0518929 and the Yrj Jahnsson s Foundation respectively We thank seminar participants at DIMACS Ohio State University University of Iowa University of Madrid and the University of Maryland for valuable comments 0 1 2 3 4 56 4 7 8 8 1 9 8 7 7 6 1 0 7 1 0 7 7 7 7 1 0 0 6 0 6 4 0 1 0 7 7 2 3 A A 0 0 7 1 0 7 1 1 7 1 6 1 7 0 0 7 B C C 6 7 B B D B 7 7 7 E E 7 E 7 C E E 7 7 E 7 7 7 7 4 7 C 7 7 C C 7 7 B B F B B 7 C C B C D 7 C 7 B C 7 B 5 7 B B G 7 B B 4 C C D C D 7 D 8 C B D D B D D 7 7 4 7 B C D B D D D 7 4 B G C C C 0 4 B 4 7 C G B C D D C B 1 B C D 6 6 7 B C C C C C C B D 0 1 B C 5 C C C 5 B C C 7 7 7 C 1 7 C 9 1 C C 0 B 7 C B C B 0 7 5 7 4 7 7 C C 4 0 0 C 0 C C B C D C C B C 0 4 0 6 0 7 B 6 0 0 0 H 0 B 7 6 0 0 0 0 1 0 7 B C D 7 C B C 5 D D 5 B C D 0 0 7 7 5 B D 0 D C 1 0 00 D 0 7 D 00 B D 7 B D 7 4 1 D 9 7 7 7 0 4 4 1 4 7 C C 7 B C 0 7 7 7 0 7 0 C 0 7 C 7 C C C 4 06 9 C D 7 0 06 0 4 0 7 0 9 1 7 00 0 0 0 4 0 0 0 7 0 B C 4 7 C 7 4 C 0 0 7 I C J K C J K C B C J K C C L 5 50 C B 0 7 C B 7 8 B C D 0 C B C 0 B C 0 0 C 06 C B B C 0 H 05 B C C C C C 0 4 1 1 9 7 7 7 0 4 0 M 0 05 0 B 2 G M 3 H 1 0 6 B 2G M 3 1 0 B 2M 3 0 L 5 0 B 2M 3 0 0 0L0 0 B 2 1 1 3 B 2 3 5 L 0 B 2G 3 6 L 55 0 B 2 1 B 1 M N 3 0 0L06 56 B 2 O G 3 60 L 0 B 2 7 1 M 3 0 L0 5 B B 2OP P M P P B P M P 1 3 0 B 2 3 L 0 0 B 2 3 1 2 2 3 H 1 6L Q 0 B 2 M M 3 45 6 76 089 B 2 1 3 5L 50 B 1
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