Differential Payments Within a Bidder Coalition and the Shapley Value

Daniel A. Graham, Robert C. Marshall, Jean-Francois Richard
Duke University

Jul 1 1987

At a second price or English auction a bidder coalition frequently distributes the gains to formation among its members via a secondary auction or "knockout". When coalition members are sufficiently heterogeneous a nested coalition structure emerges where a knockout is conducted at each level of nesting. In this paper the characteristics of the nested knockout and the factors underlying its use are investigated. Within many settings it is found that the expected payments made to members of a bidder coalition via the nested knockout are exactly equal to the Shapely value. Certain incentive compatibility problems of the nested knockout procedure are investigated as well.


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