Theory of linear and integer programming
Theory of linear and integer programming
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Network flows: theory, algorithms, and applications
Computationally Manageable Combinational Auctions
Management Science
Integer Programming for Combinatorial Auction Winner Determination
ICMAS '00 Proceedings of the Fourth International Conference on MultiAgent Systems (ICMAS-2000)
Proceedings of the first international joint conference on Autonomous agents and multiagent systems: part 1
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FC'02 Proceedings of the 6th international conference on Financial cryptography
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In this paper, we consider multi-object auctions in which each bidder has a positive reservation value for only one special subset of objects, called a necessary bundle. In the auction, each bidder reports its necessary bundle and its reservation value. The seller solves the assignment problem of objects which maximizes its revenue and decides the winning bidders who can purchase their necessary bundles for their reporting prices. We show that this auction leads to an efficient allocation through Nash equilibria under complete information when the bid-grid size is sufficiently small. We apply our results to spectrum auctions satisfying the conditions that necessary bundles are intervals of discretized radio spectrum. We show that the revenue maximization problem for the seller can be solved in polynomial time for the above auctions. The algorithm also indicates a method to choose an accepted bidder randomly when the revenue maximization problem has multiple optimal solutions. Lastly, we introduce a linear inequality system which characterizes the set of Nash equilibria.