A note on the inefficiency of bargaining over the price of a share

We study the problem of dissolving a partnership when agents have unequal endowments. Agents bid on the price of the entire partnership. The highest bidder is awarded the partnership and buys out her partners' shares at a per-unit price that is a function of the two highest bids. We show that there exists no price-setting mechanism satisfying certain mild regularity properties that is ex-post efficient, for any common prior of valuations. This result sharply contrasts the equal-endowment case in which efficient dissolution of the sort we are examining is possible through a simple k-double auction, as suggested by Cramton, Gibbons, and Klemperer (Econometrica, 1987).