An ascending vickrey auction for selling bases of a matroid

Operations Research

Volumn 59, Issue 2, 2011, Pages 400-413

  Bikhchandani, Sushil ^a   De Vries, Sven ^b   Schummer, James ^c   Vohra, Rakesh V ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF TRIER   (Germany)

^c NORTHWESTERN UNIVERSITY   (United States)

Author keywords

Auction; Combinatorial; Matroid; Multi item; Polymatroid; Vickrey

Indexed keywords

AUCTION; COMBINATORIAL; MATROIDS; MULTI-ITEM; POLYMATROIDS; VICKREY;

COMBINATORIAL MATHEMATICS; POLYNOMIAL APPROXIMATION;

SALES;

EID: 79957496869     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1100.0888     Document Type: Article

References (34)

1. Ausubel, L. M. 2004. An efficient ascending-bid auction for multiple objects. Amer. Econom. Rev. 94(5) 1452-1475. (Pubitemid 40465223)
2. Ausubel, L. M. 2006. An efficient dynamic auction for heterogeneous commodities. Amer. Econom. Rev. 96(3) 602-629. (Pubitemid 44273972)
3. Ausubel, L. M., P. R. Milgrom. 2002. Ascending auctions with package bidding. Frontiers Theoret. Econom. 1(1) 1-42.
4. Babaioff, M., N. Nisan, E. Pavlov. 2004. Mechanisms for a spatially distributed market. Proc. Fifth ACM Conf. Electronic Commerce, ACM, New York, 9-20.
5. Bikhchandani, S., J. M. Ostroy. 2002. The package assignment model. J. Econom. Theory 107(2) 377-406. (Pubitemid 36046773)
6. Bikhchandani, S., S. de Vries, J. Schummer, R. V. Vohra. 2008. Ascending auctions for integral (poly)matroids with concave nondecreasing separable values. SODA '08: Proc. Nineteenth Annual ACM-SIAM Sympos. Discrete Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, 864-873.
7. Clarke, E. H. 1971. Multipart pricing of public goods. Public Choice 11(1) 17-33.
8. Cramton, P. 1998. Ascending auctions. Eur. Econom. Rev. 42(3-5) 745-756. (Pubitemid 128713811)
9. Dawson, J. E. 1980. Optimal matroid bases: An algorithm based on cocircuits. Quart. J. Math. 31(2) 65-69.
10. Demange, G., D. Gale, M. Sotomayor. 1986. Multi-item auctions. J. Political Econom. 94 863-872.
11. de Vries, S., J. Schummer, R. V. Vohra. 2007. On ascending Vickrey auctions for heterogeneous objects. J. Econom. Theory 132(1) 95-118. (Pubitemid 44932900)
12. Edmonds, J., D. R. Fulkerson. 1965. Transversals and matroid partition. J. Res. National Bureau Standards 69B(3) 147-153.
13. Federgruen, A., H. Groenevelt. 1986. Optimal flows in networks with multiple sources and sinks, with applications to oil and gas lease investment programs. Oper. Res. 34(2) 218-225. (Pubitemid 17461677)
14. Fujishige, S. 1980. Lexicographically optimal base of a polymatroid with respect to a weight vector. Math. Oper. Res. 5(2) 186-196.
15. Grigorieva, E., P. J.-J. Herings, R. Müller, D. Vermeulen. 2007. The private value single item bisection auction. Econom. Theory 30(1) 107-118. (Pubitemid 44663446)
16. Groenevelt, H. 1991. Two algorithms for maximizing a separable concave function over a polymatroid feasible region. Eur. J. Oper. Res. 54(2) 227-236. (Pubitemid 21729720)
17. Groves, T. 1973. Incentives in teams. Econometrica 41(4) 617-631.
18. Gul, F., E. Stacchetti. 2000. The English auction with differentiated commodities. J. Econom. Theory 92(1) 66-95.
19. Helgason, T. 1974. Aspects of the theory of hypermatroids. C. Berge, D. Ray-Chaudhuri, eds. Proc. Working Seminar Hypergraphs, Columbus, Ohio, 1972. Lecture Notes in Mathematics, Vol. 411. Springer, Berlin, 191-213.
20. Kelso, A. S., Jr., V. P. Crawford. 1982. Job matching, coalition formation and gross substitutes. Econometrica 50(6) 1483-1504.
21. Korte, B., L. Lovász. 1984. Greedoids and linear objective functions. SIAM J. Algebraic Discrete Methods 5(2) 229-238.
22. Lawler, E. L. 1966. Covering problems: Duality relations and a new method of solution. SIAM J. Appl. Math. 14(5) 1115-1132.
23. Makowski, L., J. M. Ostroy. 1987. Vickrey-Clarke-Groves mechanisms and perfect competition. J. Econom. Theory 42(2) 244-261.
24. Mishra, D., D. C. Parkes. 2007. Ascending price Vickrey auctions for general valuations. J. Econom. Theory 132(1) 335-366. (Pubitemid 44932897)
25. Moore, J., R. Repullo. 1988. Subgame perfect implementation. Econometrica 56(5) 1191-1220.
26. Nagano, K. 2007. On convex minimization over base polytopes. M. Fischetti, D. P. Williamson, eds. Integer Programming Combin. Optim.-12th IPCO Conf. Proc., Ithaca, NY. Lecture Notes in Computer Science, Vol. 4513. Springer, Berlin, 252-266.
27. Oxley, J. G. 1992. Matroid Theory. Oxford University Press, Oxford, UK. Parkes, D. C., L. H. Ungar. 2000a. Iterative combinatorial auctions: Theory and practice. Proc. 17th National Conf. Artificial Intelligence, Austin, TX. AAAI Press/MIT Press, Cambridge, MA, 74-81.
28. Parkes, D. C., L. H. Ungar. 2000b. Preventing strategic manipulation in iterative auctions: Proxy agents and price adjustment. Proc. 17th National Conf. Artificial Intelligence, Austin, TX. AAAI Press/MIT Press, Cambridge, MA, 82-89.
29. Perry, M., P. J. Reny. 2005. An efficient multi-unit ascending auction. Rev. Econom. Stud. 72(2) 567-592. (Pubitemid 40473532)
30. Roth, A. E., T. Sönmez, M. U. Ünver. 2005. Pairwise kidney exchange. J. Econom. Theory 125(2) 151-188. (Pubitemid 43013122)
31. Schrijver, A. 2003. Combinatorial Optimization, 1st ed. Algorithms and Combinatorics, Vol. 24. Springer Verlag, Berlin, Germany.
32. Shanthikumar, J. G., D. D. Yao. 1992. Multiclass queueing systems: Polymatroidal structure and scheduling control. Oper. Res. 40(3, Suppl. 2) S293-S299. (Pubitemid 23710662)
33. Tse, D. N. C., S. V. Hanly. 1998. Multiaccess fading channels-part I: Polymatroid structure, optimal resource allocation and throughput capacities. IEEE Trans. Inform. Theory 44(7) 2796-2815. (Pubitemid 128739986)
34. Vickrey, W. 1961. Counterspeculation, auctions, and competitive sealed tenders. J. Finance 16(1) 8-37.