Introduction:

Partnerships form and dissolve. Examples range from marriage to business partnerships. Business partnerships are a frequent form of organization in law firms and small scale joint ventures among professionals with complementary skills.

Typically, a partnership invests in specific assets. Therefore, when one partner requests dissolution of the partnership, the best use of these assets is to grant single ownership to one of the partners, who may then continue to run the business, either alone or with a new partner.

Similarly, when the owner of a business deceases, an inheritance rule may stipulate that the firm is awarded to one of the heirs, in order to maintain undiluted incentives, with the provision that the other heirs earn some fair compensation. A dissolution rule determines the partner who shall become single owner, and the compensation to be paid to the other partner(s).

The legal literature on partnership dissolution generally advises to use a simple dissolution rule, known as “Texas shootout” or “buy-sell option” (see Mancuso und Laurence (2003)). There, the party who asks for dissolution must propose a price at which the other partner(s) may either sell their share(s) or buy the proposer’s share. These rules are now so predominantly used that “... a lawyer’s failure to recommend or include them in modern joint venture agreements is considered ‘malpractice’ among legal scholars and practitioners” (Brooks und Spier (2004)).

In contrast to the generally accepted legal advice, economists tend to favor a more even handed mechanism, such as the use of an auction, in which all partners are asked to bid for the other partners’ shares (see Cramton, Gibbons, und Klemperer (1987),McAfee (1992), and the survey by Moldovanu (2002)). However, as De Frutos und Kittsteiner (2004) have shown, the two mechanisms tend to have similar properties if the “buy-sell option” is preceded by an open, ascending-bid (English) auction, that determines who shall have the right to propose in the execution of a subsequent Texas shootout.

The present paper considers the dissolution problem of an equal share partnership, and solves the equilibrium of two simple auction rules. It is closely related to the literature on fair division games (see G¨uth und van Damme (1986))1, on partnership dissolution (see Engelbrecht-Wiggans (1994), whose results are corrected here), and to Lengwiler und Wolfstetter (2004), where we analyze some mathematically similar auction problems.