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All equilibria of the multi-unit Vickrey auction |
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| Authors: | Andreas Blume Paul Heidhues Jonathan Lafky Johannes Münster Meixia Zhang |
| Institution: | 1. National Economics University, Hanoi, Vietnam;2. Minot State University, Minot, USA;3. New Mexico State University, Las Cruces, USA;4. School of Science, Aalto University, Finland;5. School of Business, Aalto University, Finland;1. School of Management, Xi’an Jiaotong University; and State Key Lab for Manufacturing Systems Engineering, Xi’an 710049, China;2. Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, the Netherlands;3. Department of Computer Science, Georgia Southern University, Statesboro, GA 30458, USA |
| Abstract: | This paper completely characterizes the set of equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there are at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price. |
| Keywords: | Vickrey auction Multi-unit auction Ex-post equilibrium Reserve price Uniqueness Core |
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