32: Dissolving a Partnership Dynamically

Author(s): John Wooders,  Economics Discipline Group, University of Technology Sydney, Sydney, Australia. Matt van Essen 

Date of publication:  Janaury 2016 

Working paper number: 32

Abstract: In financial disputes arising from divorce, inheritance, or the dissolution of a partnership, frequently the need arises to assign ownership of an indivisible item to one member of a group. This paper introduces and analyzes a dynamic auction for simply and e¢ciently allocating an item when participants are privately informed of their values. In the auction, the price rises continuously. A bidder who drops out of the auction, in return for surrendering his claim to the item, obtains compensation equal to the di§erence between the price at which he drops and the preceding drop price. When only one bidder remains, that bidder wins the item and pays the compensations of his rivals. We characterize the unique equilibrium with risk-neutral and CARA risk averse bidders. We show that dropout prices are decreasing as bidders become more risk averse. Each bidder’s equilibrium payo§ is at least 1/N-th of his value for the item. Indeed, we show that each bidder’s security payo§ is 1/N-th of his value. We introduce the notion of a perfect security strategy, we show that each bidder has a unique perfect security strategy, and that it coincides with the equilibrium bidding strategy as bidders becomes infinitely risk averse.

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