Decision-analytic approach to knockout auctions

Society seems to have developed several ingenious schemes for allocating jointly owned indivisible items. One such scheme, occasionally used to divide estates among heirs, is a knockout auction (Engelbrecht-Wiggans 1994). In a knockout auction, the joint owners bid for the item; the highest bidder obtains it and pays the others their share of the winning bid. This paper follows the advice of Raiffa and Rothkopf to view auctions from a decision-analytic point of view, and analyzes the optimal bid of an expected-utility maximizing participant in a knockout auction who is uncertain about the bids of others, and contrasts it to the properties of optimal declarations in buy-sell agreements, derived in Gerchak and Fuller (1992).