February 5, Richard Brooks and Kathryn Spier. This paper is concerned with the dissolution of joint ventures such as closelyheld

Transcription

1 TRIGGER HAPPY OR GUN SHY? February 5, 004 Richard Brooks and Kathryn Spier. Introduction This paper is concerned with the dissolution of joint ventures such as closelyheld corporations, partnerships, and limited-liability companies where the external market for ownership interests is thin. The absence of efficient ownership markets implies that dissolution effectively leads to a private auction among the members of the venture. There are numerous ways of conducting this auction, as well as meaningful alternatives to an auction (e.g., mediation or liquidation), but we focus on a particular auctioning device known as a Texas Shootout. A Texas Shootout so labeled because once initiated (or triggered) only one party will be left standing is a buy-sell provision where a party names a price for her share of the venture and another other party decides whether to pay that price (i.e., buy out the first party) or to be paid that price (i.e., sell out to the first party). 3 See McAfee (99) and Brams and Taylor (996) for comparisons (in terms of efficiency and fairness) of various auctions that may be employed. Texas Shootouts are alternatively referred to in the literature as Texas Auctions, the Shotgun Rule, the Cake-Cutting Rule and Russian Roulette Auctions. Practitioners also refer to these devices as buy-sell and put-call options. We will, for the purpose of exposition, introduce terminology to differentiate between buy-sells and shootouts (see infra note and accompanying text). In short, shootouts are a special class of buy-sell options. 3 Some shootout agreements allow any party to trigger them for any reason, while others require the occurrence of stipulated (often verifiable) events before they can be initiated.

2 The practical implementation of a Texas Shootout is well-illustrated by the contested dissolution of Omnibus Financial Group (Omnibus). Omnibus was organized as a limited liability company (LLC) by four investors (members) in 996. Two members withdrew within two years, leaving John Valinote and Stephen Ballis as comember-managers of the venture. Valinote soon ceased participating in the venture and subsequently approached Ballis looking for an exit strategy. This led Ballis to initiate the buy-sell clause of Omnibus s operating agreement. 4 Ballis announced a value for half of the business and Valinote opted to sell his fifty percent stake, allowing Ballis to continue the business without the disruption and transaction costs associated with a negotiated separation or liquidation. 5 Because of their potential for efficient and fair dissolution of joint ventures, shootout clauses have practically become boilerplate. 6 Although shootout provisions are widely used in practice, they have received only limited attention in the academic literature. We consider a simple extensive-form game where two partners initially share joint ownership of an asset. Later, an event occurs that makes joint ownership inefficient: the value of the underlying asset is higher if one partner has sole control. Bargaining is complicated by the fact that one of the partners 4 Valinote v. Ballis, 95 F.3d 666 (7 th Cir. 000). The initiation of a buy-sell clause often imposes several formal requirements, including giving proper written notice, postings of deposits or bonds or both, and the triggering of time periods within which the other party must accept the buy-sell offer and close. A party s failure to meet these requirements may have severe detrimental consequences for that party. 5 Ballis actually announced a value of -$,58.9 per one percent interest in the business (i.e., the business had negative value) and thus by choosing to sell his interest in the business, Valinote $79,064 to Ballis. 6 The importance of buy-sell agreements is now so broadly recognized that a lawyer s failure to recommend or include them in modern joint venture agreements is considered malpractice among legal scholars and practitioners.

3 has private information about a common underlying value of the asset. 7 In our model, Texas Shootouts dissolve the partnership efficiently by removing the "status quo" of joint ownership from the bargaining table. However, though Texas Shootout contracts are jointly efficient, they are under-utilized by the partners ex post. A partner -- whether he is informed or uninformed -- can often capture greater equilibrium rents through simple offers to buy (or simple offers to sell). The threat to remain with the "status quo" of joint ownership is used strategically to extract rents in bargaining and, in the process, destroys joint value. Since private parties have an insufficient incentive to make Texas Shootout offers ex post, it is in their interest to write contracts ex ante to encourage their use. Yet, a simple contractual provision for shootouts will not assure adequate utilization, unless their use can be compelled by the parties. This important feature of the Texas Shootout has been largely overlooked by practitioners and academics. The formal economics literature has, for the most part, focused on direct revelation mechanisms for allocating partnership assets. 8 Cramton, Gibbons and Klemperer (987) first characterized the set of incentive-compatible interim-individuallyrational dissolution mechanisms in the independent private values context. They demonstrated that ex post efficient allocations may be reached where parties have roughly equal ex ante ownership stakes in the asset (such as with equal partners), unlike the case, for instance, where one party begins with complete ownership (Myerson and Satterthwaite 983). However, the Texas Shootout proved not to be an efficient 7 Texas Shootouts are unnecessary under symmetric information. Rational partners would easily negotiate a price for the sale of the asset. 8 Cf. e.g., Minehart and Neeman (999), who examine termination and coordination of activities in partnerships, and Levin and Tadelis (00), who focus on investment in partnerships and organizational form. 3

4 allocation mechanism in this context (McAfee 99; Minehart and Neeman 999). 9 Jehiel and Pauzner (00) employ a mechanism design approached to the partnership dissolution problem where parties have interdependent values and are asymmetrically informed. (See also Moldovanu 00). They find that this setting significantly restricts the range of efficient implementable mechanisms observed by Cramton, Gibbons and Klemperer (987). As the literature moved from the assumption of private values to interdependent or common values, some of the focus has shifted from bargaining efficiency to fairness concerns. See Brams and Taylor (996) for a survey of the fairness implications. 0 The focus on fairness is justified, at least implicitly, by the view that if an asset has a value that is common to all individual parties then no allocative efficiency implications are raised by an ex post assignment of ownership to one partner or the other. In our model, however, Texas Shootouts raise salient efficiency implications even in the context of common values. In this context shootouts restrict strategic behaviors that interfere with the allocation of the asset to one party or another when joint ownership is no longer desirable. Though shootouts have long been understood to restrict behaviors strategic and otherwise there remains ambiguity about the different ways they restrict and which restrictions serve efficiency. To clarify, we offer the following abbreviated taxonomy. First, at the most basic level, shootouts are merely buy-sell offers where the acceptance or 9 Ex post efficiency is achieved under full information and the parties prefer to be offerors rather than offerees, which flips under asymmetric information (McAfee 99). 0 For example, in his analysis of the fairness of shootouts Morgan (003: 4) abstracts away from efficiency considerations entirely based on the view that with common values, all allocations are efficient. 4

5 the offer is constrained by prior agreement among the co-venturers. When there are no constraints (e.g., one party may or may not issue a buy-sell offer, which another party may or may not accept) the buy-sell is not binding, involuntary or mandatory. A shootout is binding when a party may (but is not required to) make a buy-sell offer, which another party must accept. The offer is binding on the offeree because the parties have individually pre-committed to acceptance. A shootout is involuntary when a party can be compelled to make a buy-sell offer, which may be accepted by another party. Finally, without necessarily compelling offers or pre-committing to acceptances, the parties may limit themselves to exclusive use of shootouts. We call a shootout mandatory when the parties agree that no other mechanism may be used to buy or sell any individual s interest in the business. (See Table below). Our simple analysis proceeds in several steps. First, we demonstrate that buysells without restrictions are inefficient given the credible threat of maintaining the suboptimal status quo of joint ownership. Next, turning our attention to binding Buy-sell offers simply give the offeree the option of buying or selling an object at the price or prices stated by the offeror. Shootouts may also constrain both the offer and the acceptance or some other restriction may be imposed, such requiring the use of a buy-sell (which we label a mandatory shootout later in the text.). Mandatory shootouts may thus serve the useful function of preventing departing members from transferring their ownership interests to third parties without the approval of the remaining members of the venture. A more common means of limiting such transfers is, of course, a right of first refusal. A right of first refusal gives the remaining members the right to purchase the departing member s interest at the price offered to the third party. There are also often statutory constraints on transferring full ownership interests to third parties without the prior approval of the remaining parties to the venture (see e.g., the Uniform Partnership Act). We introduce mandatory shootouts (not because they are common, but) largely as an expositional tool, as will become clear later in the article. Indeed, lawyers often advice their business clients not to provide that the buysell is the only mechanism for resolving disputes. (Welborn 990: 9). 5

6 shootouts, we show that pre-committing to acceptances does not improve matters because the parties will have incentive to accept non-binding buy-sell offers in equilibrium. Therefore, binding shootouts perhaps the most commonly used in practice perform no better in terms of efficiency than a simple ad hoc buy-sell offer. 3 The problem is not that parties need encouragement to accept buy-sell offers, but rather that they need encouragement to make these offers. This encouragement may be explicitly provided through involuntary shootouts and implicitly through mandatory shootouts under certain conditions. The last part of our analysis identifies these conditions and shows the importance of involuntariness for allocative efficiency. In addition to clarifying the key restrictive aspects of shootouts, our analysis offers a number of interesting implications. In particular, we will see that the design of these contracts may vary depending on whether the parties exist in a Rawlsian world, not knowing which partner is likely to be more informed, or if they can fairly predict who will know more about the value of the business upon dissolution. Thus shootout agreements might look quite different for general partnerships, limited liability partnerships (LLPs) and member-managed limited liability companies (LLCs) as compared to limited partnerships, manager-managed LLCs and close corporations because the latter set has substantially weaker management and control rights over the business. The next section lays out the basic notation of the model. The third section considers buy-sell offers without restrictions. The equilibria are characterized where each party can make a final offer, and it is shown that buy-sell offers are underutilized. The fourth section focuses on restrictive buy-sell (i.e., shootout) clauses and argues that 3 [Note about the model buy-sell. And Surkin, Weilborn etc ] 6

7 each party will try to force the others to make the offer. A discussion and conclusion follows. Proofs, when omitted from the text, are given in the Appendix.. The Model Suppose that two partners, i =,, initially have joint ownership over an asset whose (future) value is x. Partner privately observes the value of the asset, x [0, ], which is drawn from a commonly known distribution f(x). We assume that this function positive on its support and integrable. The partners payoffs if they remain in the relationship are { x /, x / }. The value created by the asset is higher when under the sole control of one of the partners, x + a. The parameter a is assumed to be non-negative and commonly known. Although the underlying value of the asset is privately observed by Partner, it is common knowledge that gains from trade exist. The assumption that the asset creates more value when owned by one partner may be justified in a number of different ways. First, it may reflect an underlying moralhazard-in-teams problem (Holmstrom, 98) where, under joint ownership, each partner would underinvest relative to the socially efficient level. Second, it may reflect private benefits of control that are outside the model. A sole partner, for example, may gain disproportionate non-pecuniary benefits such as respect and prestige in the business community or disproportionate pecuniary benefits from invitations to serve on boards of directors. Third, the partnership may, by its very nature, require investments from each partner that are duplicative at this stage in the firm's life cycle. 4 Finally, but certainly 4 The ongoing transactions costs of filing tax returns as a partner should be higher than, say, simply liquidating the asset and purchasing shares in an index fund instead. To give an even more innocuous example, the transactions costs associated with partnerships may be higher since two signatures would be required on many partnership documents. 7

8 not least likely, the partnership may be in deadlock, 5 wherein irreconcilable differences between partners prevents the business from moving forward. 6 Demonstration of deadlock will empower a court to dissolve the partnership if a party seeks a judicial resolution, however the issue of the efficient allocation of partnership assets is not an explicit objective of such proceedings. We assume that the two partners are equally capable of running the firm alone. We adopted this assumption for purposes of exposition: the notation is simpler and the proofs are shorter as a result. Our results do extend, however, to asymmetric stakes where, for example, Partner would derive greater value from sole ownership than Partner. Indeed, many real-world examples of shootouts are instigated by the death of one of the partners. 7 We would expect that the heirs to the deceased partner's shares are in a worse position to fun the firm than the living partner. The parties subsequently negotiate to dissolve their partnership. We assume that negotiations consist of a single take-it-or-leave-it offer involving a single price ik p. Indicator i refers to the partner making the offer, i =,. Indicator k tells whether it is an offer to buy at the given price (B), an offer to sell at that price (S), or a "Texas Shootout," 5 The generic definition of deadlock is a complete standstill; lack of progress due to irreconcilable disagreement or equal opposing forces (OED). In a legal proceeding, a determination of deadlock allows the court to dissolve the joint venture agreement discharge appropriate remedies. 6 Deadlock is a salient concern in corporations and LLCs, as well as in partnerships. Deadlock in a closely held corporation arises when a control structure permits one or more factions of shareholders to block corporate action if they disagree with some aspect of corporate policy. Black s Law Dictionary. 7 Kathy, I will find a sample case or two for this claim. 8

9 which gives the receiver the option to buy or sell at the named price (T). 8 We will also let π ik j ( x ) denote the probability that Partner j ends up owning the asset given the offer of type k made by Partner i, and S ik j ( x ) denote Partner j's surplus, or his payoff above the joint ownership payoff x/. 3. Voluntary & Non-Binding Buy-Sell Offers In this section we assume that there is no pre-existing contract allowing for the use of the Texas Shootout. Instead, the parties have the option to make a Texas Shootout offer and will do so if (and only if) it is in their private interest. The partners' reluctance to use the shootout may be illustrated for the special case where x is commonly known -- the two partners are symmetrically informed during negotiations. Partner 's best shootout offer, T p, may be found by backwards induction. Partner will sell to partner if p T T > x + a p or T p x+ a > and will buy otherwise. (Note that Partner prefers at least one of these two outcomes -- selling or buying -- to remaining with the status quo and receiving x/.) Working backwards in time, the best offer (from Partner 's perspective) makes Partner indifferent between buying and selling: T p x+ a =. In equilibrium, the two partners share the bargaining surplus T T = equally: S ( x ) = S a /. It is easy to see why Partner will never voluntarily 8 A more general framework would allow for offers to buy and sell at different prices, The full analysis of this more general case is more complicated and left for future research. 9

10 choose the Texas Shootout. Partner can extract all of the bargaining surplus through a simple offer to buy Partner out for a price p B = x / (plus a penny, perhaps). 9 When asymmetric information is introduced, Texas Shootouts actually create social value. We will see that simple offers to buy or sell create bargaining breakdowns where status quo is maintained. The shootout serves to remove the inefficient status quo from the bargaining table and, in doing so, guarantees that the bargaining surplus, a, is jointly captured by the two partners. Although the Texas Shootout is in the partners' joint interest, it will be underutilized by the private parties in equilibrium. As in the simple example with symmetric information, the partners may be able to capture a greater share of the bargaining surplus through the simple offers to buy or sell. 3. The Informed Partner Makes the Offer This section characterizes the fully separating equilibrium that arises when Partner, the informed partner, can make a take-it-or-leave-it offer. Partner offers to sell his shares to Partner when the parameter x is sufficiently low and offers to buy Partner 's shares when the value of x is sufficiently high. In an intermediate range, however, Partner will voluntarily choose a Texas Shootout. Proposition : There is a unique separating equilibrium when the informed partner, Partner, makes a take-it-or-leave-it offer to Partner. Let x ˆ = min{/, aln(4)}. 9 In this case, S ( x ) = a and S ( x ) = 0. Equivalent payoff would obtain if Partner offered to sell his share for for p S + = x / a. 0

11 i. If x xˆ Partner offers to sell his shares to Partner for p S ( x) = x / + a ; ( x) x / a π = e π ( x ) = 0, x / a S ( x ) = ae and S ( x ) = 0. ii. If x ( xˆ, xˆ ] Partner offers a Texas Shootout: p T ( x) = ( x + a) / ; π T T = T T = ( x ) = π ( x ) /, and S ( x ) = S ( x ) a /. iii. If x > xˆ Partner offers to buy Partner 's shares for p B ( x) = x / ; ( x) ( x)/ a π = e, π ( x ) = 0, ( x ) / a S ( x ) = ae and S ( x ) = 0. This separating equilibrium may be understood intuitively. Let's first consider Partner 's simple offer to sell his shares to Partner. We see in part (i) of the proposition that if x = 0 (so the asset is worthless when owned jointly) that Partner offers p S (0 ) = a and Partner accepts with probability π (0 ) =. Partner is in effect admitting that his has a lemon Partner has no reason not to believe him! Now suppose that x is slightly higher so Partner 's offer is above a. Partner cannot accept with certainty; if he did, then Partner would make the higher offer when x = 0 as well! Indeed, the separating equilibrium has the feature that Partner randomizes between accepting p S ( x) = x / + a for all x > 0. Partner is, of course, indifferent between accepting and rejecting in equilibrium: if he rejects the offer he gets the status quo payoff of x/, and if he accepts he gets the same thing: x + a p ( x ) = x /. Several observations are in order. When Partner makes a simple offer to sell, Partner 's probability of acceptance, π ( x) = e x / a, is falling in the common value of the asset, x. Intuitively, Partner is very happy to accept the offer where Partner admits to having a lemon of the very worse variety. But when Partner 's offers are

12 higher -- signally that the value x is higher as well -- then a lower probability of acceptance is necessary in order to maintain incentive compatibility for Partner. This lower probability of acceptance is what prevents Partner from exaggerating and pretending to have a plum rather than a lemon. It is also important to notice that Partner is capturing equilibrium rents. (Partner, on the other hand, is indifferent between purchasing the shares and remaining with the status quo of joint ownership.) Furthermore, Partner 's rents are higher when the value x is smaller. This may be seen most clearly when x = 0 for in this case Partner captures the entire bargaining surplus a! Finally, when x is very high, Partner captures low rents from a simple offer to sell. When x is high, Partner will forego the offer to sell in favor of an offer to buy. We see in part (iii) of the proposition that when x = -- its highest level -- Partner would offer to buy Partner 's shares for / and Partner would surely accept. There is no reason for Partner to be dubious here -- / is an excellent price! Notice that Partner extracts all of the surplus, a, through this offer. The probability of acceptance, π ( x) = e ( x)/ a, is rising in the Partner 's offer. Again, this is necessary to maintain incentive compatibility. Notice that Partner 's rents are rising in x, the value of the asset. Now suppose that Partner, the informed partner, makes a Texas Shootout offer with price, T p. Partner can buy that price, giving the two partners payoffs { p T T T T, x + a p }, or can sell at that price giving payoffs { x + a p, p }. The separating equilibrium with the Texas Shootout has a particularly simple form. Partner offers to split the value fairly with the uninformed partner, p T ( x) = ( x + a) /. Note that this offer makes Partner indifferent between buying and selling. Partner subsequently flips an evenly weighted coin to determine whether to buy or sell:

13 T = π ( x) /. 0 Partner is, in fact, indifferent among the offers here and is happy to "tell the truth." Note that, in equilibrium, Partner and Partner share the bargaining surplus, each receiving a/. Partner is "gun shy" in Proposition, avoiding the Texas Shootout at the extremes of the distribution. It is not hard to see why. Suppose that Partner knows that the asset is a plum: x =. With the Texas Shootout he offer p T () = ( + a) / and captures half of the surplus, a/. He can do strictly better with a simple offer to buy. Suppose he offers to buy the asset for p = / (plus a penny perhaps). This is an excellent offer from Partner 's perspective: the outside option is x/, which is dominated by Partner 's offer for any beliefs that Partner holds. Partner will certainly accept the offer and sell to Partner. Partner has paid / for an asset that is worth / + a, capturing the entire surplus! Similarly, if x = 0 then Partner can capture the whole surplus by making a simple offer to sell the asset for p S (0) = a. 3. The Uninformed Partner Makes the Offer Suppose instead that the uninformed partner, Partner, makes a take-it-or-leave-it offer to Partner. We will first characterize Partner 's best Texas Shootout offer. Next, we will prove that Partner will never choose to invoke the shootout -- the Texas Shootout is dominated by either a simple offer to buy or a simple offer to sell. 0 It is straightforward to verify that Partner would never exercise the third option: refusing to buy or sell and receiving the status quo instead. For any set of beliefs, one can verify that he would strictly to prefer to either buyer or sell. Plus a penny, perhaps. As before, Partner will accept this offer regardless of his beliefs. 3

14 Consider a Texas Shootout where Partner names a price T p. Partner can subsequently buy Partner 's share for price T p giving the two parties payoffs T T { x + a p, p }, or sell her share to Partner for the same price giving payoffs { p T T, x + a p }. Being well informed, Partner will "buy" instead of "sell" when T T T T x + a p > p or x x = p a. Partner 's problem would be to find the optimal cutoff, T T ( T a x, and corresponding offer, p = x + ) /, to maximize his expected payoff: T z x = arg max [ x + a ( z + a) / ] f ( x) dx + [( z + a) / ] f ( x) dx. z 0 T Differentiating this expression, x (0,) is uniquely defined by F ( x ) = 0. z T p T + Proposition : Partner 's best Texas Shootout offer, = ( x a ) /, corresponds to the median of the type distribution, x. (i) If x < x then Partner sells his shares to Partner. π T ( x ) = 0, π T ( x ) =, S T ( x ) x x + a =, and S T ( x x + a x ) =. (ii) If x > x then Partner buys Partner 's shares. π T ( x ) =, π T ( x ) = 0, S T ( x x + a x ) =, and S T ( x x + a x ) =. Partner would never choose to ignore the offer altogether and stay in the relationship instead. If p T < x / then Partner prefers buying out Partner to the status quo (where he gets x/). If p T > x / the Partner prefers selling out to Partner to receiving the status quo payoff of x/). 4

15 Note that the Texas Shootout is not a particularly attractive mechanism from Partner 's perspective. If the asset is a "plum", x > x, then Partner will buy out Partner at an "average" price. If the asset is a "lemon," x x, then Partner sells out an average price and Partner is stuck with a less valuable asset. In both cases, Partner is getting the short end of the stick (so to speak). Despite the fact that the Texas Shootout may be desirable for the two partners jointly, Partner will never find it in his individual interest to use the shootout -- he is "gun shy." It is easy to see why. Partner 's payoff from the Texas Shootout is x xf ( x) dx + a /. 0 Suppose instead that Partner makes a simple offer to sell for x / + a. Partner would accept this offer if x is above the median and would reject the offer if x is below, the same cutoff as in the Texas Shootout. 3 Partner 's payoff from this sell offer is: x ( x / ) f ( x) dx + (/ )( x / + a). 0 Comparing these two payoffs verifies that Partner strictly prefer the simple offer to sell to the Texas Shootout. 4 A similar argument can be made to show that he would also prefer a simple offer to buy. 5 3 If Partner accepts the offer Partner receives payoff x + a ( x / + a) and if he rejects he receives x/. 4 This is not Partner 's best offer. It is not difficult to show that he would make an offer p S S S S = x / + a where F ( x ) af ( x ) = 0. 5 B B B B The best offer to buy would involve p = x / where af ( x ) F( x ) = 0. 5

16 Proposition 3: The uninformed partner, Partner, would prefer to make a simple offer to buy the asset (or a simple offer to sell the asset) to making a Texas Shootout offer. Intuitively, Partner would rather use the simple offer to buy or the simple offer to sell to create a threat of breakdown for Partner. This threat strengthens Partner 's private incentive to accept hard-ball offers. Although this lead to inefficient breakdowns in equilibrium, it increases Partner 's share of the bargaining surplus ex post. 4. Shootouts The results of the last section suggest that buy-sell offers are efficient mechanisms for dissolving partnerships, but will be underutilized by the private parties once they are in a position of asymmetric information ex post. It is therefore in their interest to write contracts ex ante allowing for the use of these mechanisms. However, even though provided for contractually, our analysis will now show that parties have insufficient incentive to trigger these mechanisms, which increases the likelihood of inefficient continuation of joint ownership of partnership assets. 6 Consider, as an illustration of this point, the well-known case of Owen v. Cohen (94), 7 involving the dissolution of a bowling-alley partnership in Burbank, California. After enduring several breaches of the partnership agreement and personal mistreatment by Cohen, 8 Owen 6 The uninformed partner prefers to make a simple offer to buy or a simple offer to sell and the informed partner prefers the Texas Shootout only over an intermediate range of values. 7 9 Cal.d The court found that in addition to shirking his management responsibilities (allegedly informing Owen that he had not worked yet in 47 years and he did not intend to start now ), Cohen wrongly appropriated partnership funds, sought to open an illegal 6

17 demanded that his partner make an offer either to buy out his [Owen s] interest in the business or to sell to him. In flatly rejecting this solicitation, Cohen observed that it would cost [Owen] plenty to get rid of him. Cohen s reluctance to make the buy or sell offer to Owen provides some insight into how shootout clauses ought to be structured. In practice, shootouts often do not to account for parties reluctance to make buy-sell offers. Shootouts are typically binding, which means that the offeree must either accept the offer to buy or the offer to sell and the court may use its equitable powers to compel this verifiable outcome in the face of resistance. 9 Thus, once the offer is made the inefficient status quo of joint ownership is taken off the table. However, as shown above, the parties will be hesitant to make the offer in the first place. Therefore inefficiencies will result unless the shootout is mandatory (i.e., a shootout must be used) or involuntary (i.e., a party may be compelled to make the offer). Whether, and under what circumstances, parties will agree to have their hands force in this manner is the focus of the next section. We begin this part of the analysis with binding shootouts. 4. Binding Shootouts Once this phase is entered and a buy-sell offer has been made, the offeree must either accept the offer to buy or the offer to sell and the court may use its equitable powers to compel this verifiable outcome in the face of resistance. 30 {Repeat description of binding shootout] When the informed partner, Partner, makes a binding shootout gambling room on the second floor of the bowling alley property, and engaged in persistent efforts to humiliate [Owen] before the employees and customers of the bowling-alley. 9 The court may also award some remedy or the agreement itself may stipulate liquidated damages 30 DESCRIPTION OF THE MODEL SHOOTOUT! 7

18 offer, the uninformed partner s best response is to randomize between buying and selling at the offer price. In equilibrium, the two partners split the available surplus: E( S T T a ) = E( S ) = /. When the uninformed partner, Partner, makes the binding offer, the surplus is not divided evenly because Partner earns information rents: If p T > ( x + a) / then Partner would sell and earn more than a/; if the price p T < ( x + a) / then Partner would buy and earn more than a/. The expected surpluses may be written as: E( S E( S T a x ) = a / + xf ( x) dx x / > / and x T a 0 ) = a / + xf ( x) dx x / < /. Each partner would prefer the other to be the one to "pull the trigger". 4. Must Use Shootout This section will consider several contractual forms with the common feature that dissolving the partnership using any mechanism other than a shootout is prohibited. 3 Suppose that the two partners were given the option, but not the obligation, to name a price. The preceding comparison suggests a stalemate, where each partner waits for the other partner to pull the trigger. Indeed, we would expect to see delay in these settings as each partner tries to convince the other partner to make the offer instead. This type of contract may lead to immediate resolution in some circumstances, however. When a = 0, note that Partner 's surplus from the Texas Shootout is negative: 3 Enforcement of such an agreement may require the involvement of a third party who would receive payments if the two partners ever deviated and negotiated a side deal. 8

19 T x S = xf ( x) dx x / < 0 0. Partner prefers to remain in the relationship earning x / than to pull the trigger. More generally, when the parameter a is small then the uninformed partner will refuse to make a Texas Shootout offer. 3 In these circumstances, Partner would bite the bullet, pull the trigger, and share the surplus. 4.3 Involuntary Shootouts (Forcing the Other Partner to Pull the Trigger) Suppose that each partner has the right to either pull the trigger themselves or force the rival to pull the trigger. It is clear that both partners would want to force the other to do it. There would be no inefficient delay here, since neither wants to be the one holding the gun. 4.3 Discussion Given the surplus generated by involuntary triggers in the context of asymmetric information, ex ante the parties will have incentive to allocate rights to at least one party to force the other to initiate the shootout. Call these trigger rights. Our simple analysis suggests that the trigger rights are likely to be possessed by the uninformed party, who is able to earn a premium by forcing the informed party to make the shootout offer. In particular, when parties begin joint venture knowing that one party will be less informed about the value of the asset than the other, ex ante transfers can be made for the trigger rights. Since non-managing investors (such as, for example, limited partners) have weaker management and control rights over the assets and are less likely to participate in 3 The proof is simple. Partner is indifferent between making the Texas Shootout and x remaining silent when [ x + a] f ( x) dx = x / or a = a = x xf ( x) dx. 0 * x 0 9

20 the business than managing investors (e.g., general partners), the parties can predict at the start of the relationship that non-managing investors will often, though not always, be less-informed. Thus limited partners, members in manager-managed LLCs and nonparticipating shareholders in closely held corporations should be willing to pay for trigger rights given their informational disadvantage. Similarly, it should be more difficult to allocate trigger rights in ventures where investors do not begin with this informational disadvantage, such as general partnership, member-managed LLCs and LLPs. Appendix 0

21 Proof of Proposition : Suppose Partner makes a simple offer sell his share to Partner for price p S. Partner can accept the offer giving the two partners payoffs { p, x + a p }, or reject the offer giving the two parties their joint ownership payoffs { x /, x / }. In the fully separating equilibrium, Partner is indifferent and randomizes between accepting and rejecting the offer. Indifference between accepting and rejecting the offer requires that p S ( x) = x / + a -- Partner gets none of the surplus. To find the probability of acceptance, suppose that Partner 's true type is x but he offers x p S = ( ~ x / ) + a, his payoff is π ( ~ x )[( ~ x / ) + a] + [ π ( ~ x)]( / ). Differentiating this expression with respect to x ~ and rearranging terms gives dπ ( ~ ( ~ x) ) [ ~ π x x + a x ] + 0 dx =. In equilibrium, Partner perfectly reveals his type through the offer so ~ x = x. Substituting and setting the expression equal to zero gives a first-order differential equation: dπ ( x) a + π ( x) = dx 0. Now we can solve the differential equation to get the acceptance probability. In general, ) x / a the function must satisfy π ( x = ce where c is an arbitrary constant. Partner 's surplus is S π x ( x) = ( x) a. Since π ( ) is decreasing in x it will bind at the bottom = where π (0) and so we have c =. Partner receives surplus S ( x) x / a = ae. Suppose instead that Partner makes an offer to buy the asset. In a perfectly separating equilibrium partner must randomize between accepting and rejecting, so p B ( x) = x /, Partner 's outside option. Suppose that Partner 's true type is x but he offers p B = ~ x /. His expected payoff would be ( ~ ~ / π x)( x + a x ) + [ π ( ~ x)]( / ). Differentiating this expression with respect to x x~ and rearranging terms gives x dπ ( ~ x) [ x dx ~ π ( ~ ) + a x ]. In equilibrium Partner chooses p B ( x) = x / so ~ x = x. Substituting into the expression above and rearranging terms gives first-order differential equation:

22 dπ ( ) x B a π ( x) dx = 0. Now we can solve this to get the acceptance probability. In general, the acceptance function must satisfy x) x / a π ( = ce where c is an arbitrary constant. Partner 's surplus is S π x ( x) = ( x) a. Since π ( ) is increasing in x it will bind at the top where π () =, so / a c = e and ( x) ( x) / a π = e. Partner receives surplus S ( x) ( x) / a = ae. x T x Finally, S ( x) S ( ) if and only if x / ; S ( x) S ( ) if and only if T x x aln(4) ; S ( x) S ( ) if and only if x aln(4). Q.E.D.

23 Bibliography Brams, A. and A. Taylor, 996. Fair Division: From Cake-Cutting to Dispute Resolution. New York: Cambridge University Press. Cramton, P., Gibbons, R. And P. Klemperer, 987. "Dissolving a Partnership Efficiently," Econometrica, Vol. 55, pp Holmstron, B. 98. "Moral Hazard in Teams," Bell Journal of Economics, Jehiel, P. and A. Pauzner, 00. "Partnership Dissolution with Affiliated Values," Tel Aviv University Discussion Paper. Levin, J. and S. Tadelis, 00. "A Theory of Partnerships." Stanford University Mimeo McAfee, R. P. 99. "Amicable Divorce: Dissolving a Partnership with Simple Mechanisms," Journal of Economic Theory, Vol. 56, pp Minehart, D. and Z. Neeman, 999. "Termination and Coordination in Partnerships," Journal of Economics & Management Strategy. Vol. 8 (). p 9-. Moldovanu, B. 00. "How to Dissolve a Partnership," Journal of Institutional and Theoretical Economics, Morgan, John "Dissolving a Partnership (Un)fairly," Economic Theory (forthcoming). Myerson, Roger and Mark Satterthwaite, 983. "Efficient Mechanisms for Bilateral Trading," Journal of Economic Theory, Vol. 9, pp