Contractual incompleteness and the optimality of equity joint ventures

Journal of Economic Behavior & Organization Vol. 37 (1998) 391±413

Contractual incompleteness and the optimality of equity joint ventures Sudipto Dasguptaa, Zhigang Taob,* a

Department of Finance, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong b School of Business, The University of Hong Kong, Pokfulam Road, Hong Kong Accepted 4 June 1998

Abstract Firms engaged in the pooling of complementary skills often choose the Equity Joint Venture (EJV) over alternative profit-sharing arrangements. This paper addresses the issue of how equity shares are different from profit shares. It is shown that, in settings of contractual incompleteness, marketable equity ownership, when compared to non-transferable profit-sharing contracts, provides better ex ante incentives to the parties involved by mitigating ex post hold-up problems. Among other things, the prevalence of the 51±49 or 50±50 EJV in which one party has 51 percent (or 50 percent) equity shares is explained. # 1998 Elsevier Science B.V. All rights reserved. Keywords: Incomplete contracts; Equity shares; Pro®t-sharing contracts; Equity joint ventures; Wholly-owned subsidiaries JEL classi®cation: L22; D23

1. Introduction When two firms possessing complementary capabilities for developing new technologies or new products initiate joint projects, the choice of the organizational form is an issue. One of the most commonly observed forms is an Equity Joint Venture (EJV).1 In this paper, we ask the following question: what are the circumstances under * Corresponding author. Tel.: +852-2857-8223; fax: +852-2858-5614; e-mail: [email protected] 1 For example, Hagedoorn (1990) finds that for a sample of 1163 R&D cooperations for the period of 1985± 1988, the joint venture form is used in 30 percent of the cases. Veugelers (1993) finds that the joint venture form is used in 62 percent of the 668 technology alliances reported in the Belgian and the international press between 1986 and 1992. 0167-2681/98/$ ± see front matter # 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 2 6 8 1 ( 9 8 ) 0 0 1 1 7 - 6

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which firms engaged in developing new technologies or processes would choose an EJV over a simple contractual arrangement, whereby one of the firms could hire the other to perform the same tasks that the latter would perform if it were a partner in an EJV? As an example of the type of contractual arrangement that could be possible, one can imagine one of the firms (say Firm 1) setting up a wholly-owned subsidiary (WS) and offering an incentive contract (a profit-sharing scheme) to the other party (the `agent') that would relate the latter's compensation to the profits of the subsidiary. To all intents and purposes, setting up an EJV instead would seem to do essentially the same thing: it would allow the partners to share the profits of the separate entity through ownership of equity shares. Thus, the basic question is: why are equity shares different from simple profit shares? We argue that the difference stems from the fact that a joint venture partner enjoys somewhat different rights over future profit streams than an agent of a WS. The most important difference here is that equity is marketable,2 whereas profit shares promised as part of an incentive scheme typically are not. The agent of a WS is promised profit shares as part of a document that represents an agreement between the two parties. It is difficult, if not impossible, to separate the profit claims from the rest of the agreement and market them. Equity shares afford a simple way to implement this separation. We show that this distinction is in fact crucial for understanding the difference between an EJV and a WS, and why the former may do better than the latter under some circumstances. We argue that the marketability of equity can mitigate ex post opportunism by the other partner that may otherwise arise and lead to inefficient outcomes.3 From Grossman and Hart (1986), we know that the allocation of rights matters in the presence of contractual incompleteness.4 In the context of projects involving the development of new technologies or innovations, contractual incompleteness arises for a very natural reason: not all the future products (innovations) can be foreseen ex ante. Typically, such projects have certain well-defined technological milestones or objectives, but often there are spin-offs that were not anticipated ex ante. These unforeseen applications could be in market segments in which one of the partners is a dominant player and has an incumbency advantage ± essentially precluding entry by the other.5 The inability to specify precisely ex ante the full range of future applications makes it impossible to write contracts based on the sharing of the profits from these applications, which accrue to the partners in their existing lines of business and thus cannot automatically be shared. We show how the rights associated with equity matter in the 2

Some important qualifications apply, which we discuss in Section 3.2.1 of the paper. We should add that the choice of organizational/contractual mode is obviously not limited to an EJV or a simple contractual arrangement. One alternative is to simply acquire the other firm. Vertical integration, however, has several well known costs (see Grossman and Hart (1986) and Hart and Tirole (1990)). Also, we should note that while the formation of a WS is not strictly necessary for a contractual arrangement, there may be some advantage to doing so for contracting on profits from the joint project. 4 See Hart (1995), Maskin and Tirole (1996), and Segal (1996) for the theoretical foundations of the incomplete-contracts theory of the firm. 5 In the case of cross-border collaborations such as between US and Japanese firms, one partner's home market may not be readily accessible to the other. 3

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presence of contractual incompleteness of this nature. The optimality of EJVs under certain conditions thus provides a rationale for partial ownership, an element that is missing in Grossman and Hart's analysis. Our paper is related to a growing literature on the organizational form for R&D cooperation, which will be discussed in the conclusion. In terms of research methodology, our paper is related to Aghion and Tirole (1994) as both papers analyze partial ownership in settings of incomplete contracts. In Aghion and Tirole's model, a research unit makes an innovation that is specific to its customer. If the customer has to make a cash injection into the project, it may be in the interest of the customer to demand that the research unit raise cash from third parties by selling equity shares before its research effort is made (i.e., ex ante marketability of equity). In contrast, our paper elucidates how the rights associated with equity including ex post marketability can bring about the right alignment of incentives and hence alleviate the ex post hold-up problem. Thus, while Aghion and Tirole consider only ex ante marketability of equity shares, we stress the role of ex post marketability of equity. The rest of the paper is organized as follows. Section 2 outlines the model and derives the second-best solution to a double-sided moral hazard problem. In Section 3, the optimality of equity joint ventures over alternative contractual forms is established, and the prevalence of the 51±49 (or 50±50) joint venture is explained as well. In Section 4, certain generalizations are considered. The paper concludes with Section 5. 2. The double-sided moral hazard problem 2.1. Model primitives 2.1.1. Technology We label the two partners Firm 1 and Firm 2. Both firms are assumed to be risk neutral. The firms need to provide costly effort for the success of the joint R&D project. The `state' of the project could be either `success', with probability (e1, e2), or `failure', with probability 1 ÿ (e1, e2), where e1 denotes the unverifiable effort of Firm 1 and e2 that of Firm 2. For simplicity of analysis,  is assumed to be  ˆ e1e2, where e1, e2 2 [0, 1]. The cost for firm i of effort ei is ci …ei † ˆ

i …1‡ i †= i e ; …1 ‡ i † i

where 0 < i < 1 and i ˆ 1, 2. The cost function is convex, and its first-order derivative is 1= ei i . As ei  1, a lower -firm is characterized as a `more productive' one. The restriction < 1 is thus a lower bound on the productivity of the firms and is needed for our later analysis. The above specification of  captures Hagedoorn's (1993) finding that technology complementarity is one of the major reasons for technology cooperation. It also illustrates the double-sided moral hazard nature of cooperative R&D. Notice that the project could fail even when both parties have positive effort levels and thus it is impossible for a third party to infer the firms' effort levels from the failure of the joint project.

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Fig. 1. Sequence of events.

2.1.2. Information structure, project payoffs, and contractual capabilities It is helpful to think in terms of four points of time, t ˆ 0, 1, 2, 3 (see Fig. 1 for illustration). The project involves the development of certain targeted products, for which effort has to be chosen at t ˆ 0. We will assume that the targeted products, if successfully developed, will generate a profit of V. V will be realized at t ˆ 2, and is assumed to be observable and verifiable. If unsuccessful, the project will yield a payoff of zero. All this is known at t ˆ 0. If successful in developing the targeted products, the project may also generate some exclusive benefits for the two firms (e.g., spin-offs or new products that can be used in their existing lines of business or market segments not accessible to the partner) that are unforeseen ex ante. In other words, these potential spin-offs from the project are sufficiently far off into the future that at t ˆ 0, the parties are only vaguely aware of them. These benefits are assumed to accrue at t ˆ 3. We assume that no further unverifiable joint effort is needed for the realization of these exclusive future benefits; however, the development of these unforeseen applications6 is contingent on co-operation of both firms, which may require verifiable resource contributions by the partners, and/or utilizing existing patents owned by the partners (that is to say, neither party can unilaterally develop the unforeseen products to realize its exclusive benefits).7 6 For the unforeseen products, we use the adjectives `unforeseen', `unanticipated', and `new' interchangeably, and we also sometimes refer to these products as innovations, patents, or applications. 7 In a case study about Fuji Xerox (in the business of xerographic products), an equity joint venture between Fuji Photo Film and Xerox, Gomes-Casseres (1996) gives an excellent account of how the two joint venture partners formed another joint venture, called Xerox International Partners, to engage in a new business (low-end laser printer). Bleeke and Ernst (1995) find that, in nearly 80% of their joint venture sample, one partner buys out the others in order to pursue some spinoffs from the initial joint venture business. Anecdotal evidence suggests that unforeseen spinoffs from R&D joint ventures may depend on the partners' existing technologies or agreements. See Kogut (1988) for the case of Honeywell-Ericsson joint venture and Cohen (1995) for the case of Sino-foreign joint ventures.

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Importantly, however, since it cannot be foreseen in advance what the nature of these resource contributions may be or which patents may be required, there cannot be any preexisting contracts written at t ˆ 0 that force the parties to co-operate in the development of these unforeseen products. We will assume that the realization of these future benefits are not verifiable by any third party such as the court. As is standard in the literature on contractual incompleteness (see, for example, Grossman and Hart (1986)), we assume that while the unforeseen products themselves are not specifiable ex ante, the magnitude of potential benefits to the two firms is known. Conditional on the successful development of the targeted products and cooperation of both firms in contributing verifiable resources or existing patents, the future benefits for Firm 1 are either S1 with probability 1, or zero; those for Firm 2 are either S2 with probability 2, or zero. We define V1  1S1 (henceforth the Firm 1's expected non-contractible profits) and V2  2S2 (henceforth the Firm 2's expected noncontractible profits). At t ˆ 1, each party learns whether the payoff at t ˆ 2 would be V or 0, and in the former event, the magnitude of the exclusive benefits to each party (i.e., whether positive or zero) that would be realized at t ˆ 3. However, if either of the partners at this point abandons the project, the project fails at t ˆ 2 and generates zero payoff.8 We assume that it is impossible for the courts to verify ± either at t ˆ 1 or at t ˆ 2 if the project is abandoned at t ˆ 1 ± whether the state of the project was `success' or `failure'. The strategy of our analysis is as follows: in Section 2.2, we characterize the optimal solution to the problem of pooling complementary skills between Firm 1 and Firm 2 assuming that there are no restrictions on the contractual capabilities imposed by the unverifiability of project payoffs. In particular, given risk neutrality, it is apparent that this is equivalent to assuming that the state of the project can be verified and contingent payments can be imposed. In Section 3, we examine whether, given the limitations on contractual capabilities imposed by the information structure, the optimal solution can still be implemented. The relative performance of the alternative organizational forms identified above is then examined. 2.2. The second-best outcome In this subsection, we examine the optimal solution to the problem of pooling complementary skills between the two firms, assuming that the state of the project can be verified and contingent payments can be imposed. Because of risk neutrality, we can restrict ourselves to payments in expected values. Let R(V ‡ 1S1 ‡ 2S2 ˆ V ‡ V1 ‡ V2) be the project's total expected profits, conditional on the success of the project, which occurs with probability e1e2. We normalize by setting R ˆ 1.

8

This is in spite of the fact that unverifiable effort has already been sunk. Failure would come about if, for example, the party fires important employees, hides the generated knowhow, etc. Why such `sabotage' might happen will become clear below.

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Without losing generality, it is assumed that Firm 1, which initiates the contract, has all the ex ante bargaining power.9 Firm 1 offers Firm 2 a contract {X, Y; K}, where X is the payoff Firm 1 receives contingent on the success of the project, Y is a payment from Firm 2 to Firm 1 contingent on the failure of the project, and K is an ex ante lump-sum transfer from Firm 2 to Firm 1 independent of the state of the project (all three variables are unrestricted in sign). Correspondingly, Firm 2's payoff is 1 ÿ X if the project is successful and ÿY if the project fails. For given X, Y and e2, Firm 1 chooses effort e1 to maximize its payoff e1e2X ‡ (1 ÿ e1e2)Y ÿ c1(e1), which gives e1 ˆ (e2Z† 1 , where Z  X ÿ Y. Given X, Y and e1, Firm 2 chooses effort e2 to maximize its payoff e1e2(1 ÿ X) ‡ (1 ÿ e1e2)( ÿ Y) ÿ c2(e2), which gives e2 ˆ (e1(1 ÿ Z)† 2 . Thus, for any given Z, there exists a unique pair of Nash equilibrium efforts  1=…1ÿ 1 2 † ^e1 ˆ …1 ÿ Z† 1 2 Z 1 ; (1)  1=…1ÿ 1 2 † ^e2 ˆ Z 1 2 …1 ÿ Z† 2 :

(2)

Firm 1 can extract an ex ante lump-sum transfer K from Firm 2. Assuming zero reservation utility for Firm 2, we have ^ ˆ ^e1^e2 …1 ÿ X† ‡ …1 ÿ ^e1^e2 †…ÿY† ÿ c2 …^e2 †: K

(3)

Firm 1 chooses Z to maximize its total payoff ^ ˆ ^e1^e2 ÿ c1 …^e1 † ÿ c2 …^e2 † ^e1^e2 X ‡ …1 ÿ ^e1^e2 †Y ÿ c1 …^e1 † ‡ K subject to conditions (1) and (2). Let Z* denote the optimal Z. We have the following lemma to characterize Z* assuming that the state of the project can be verified and contingent payments can be imposed. Lemma 1. For any i 2 (0, 1) where i ˆ 1, 2, the optimal success-contingent payoffs (net of the payoffs contingent on failure) for Firm 1 and Firm 2 (Z* and 1 ÿ Z* respectively) are unique and interior, and satisfy the following condition:  1=2 Z 1 ˆ (4) …1 ÿ Z  † 2 Proof. See Appendix. Notice that there is a degree of freedom in the optimal scheme, since it only uniquely determines Z ˆ X ÿ Y. Z is the `incentive' or incremental reward to Firm 1 for the success

9 None of our conclusions would change if Firm 2 has all the bargaining power. In general, the two parties can bargain non-cooperatively over the optimal contract in a Rubinstein approach. With an ex ante lump-sum transfer, the total surplus is always maximized as if one of the party has all the bargaining power and designs the optimal contract; the lump-sum transfer reflects the relative bargaining powers of the two parties. See Tao (1995) for details.

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of the project as opposed to its failure. The optimal solution indicates that the less productive a firm, the more incentive it needs to be provided. and eFB For comparison, the first-best effort levels, denoted by eFB 1 2 , maximize e1e2 ÿ c1(e) ÿ c2(e2), and it can be easily checked that both of these are equal to one. It can also be shown that ^e1 …Z  † and ^e2 …Z  † are less than one. Thus, the optimal Z* (characterized in Lemma 1) is the second-best solution.10 The double-sided moral hazard problem of cooperative R&D is a simple version of moral hazard in teams, which has been extensively studied. Holmstrom (1982) showed that, when the partners' effort levels are substitutes and not verifiable, there do not exist division rules that are budget-balancing and induce the first-best effort levels. However, there are important exceptions. One is that the partners' efforts are complements or sufficiently different (Radner (1991) and Vislie (1994)). Another is that the partners' effort levels are partially observable and/or the resulting outcomes are separately contractible (Gandal and Scotchmer (1993) and Morasch (1995)). First-best could also be achieved when partners make efforts sequentially and buyout is possible (Demski and Sappington (1991)). 3. Alternative contractual/organizational forms In this section, we examine the relative merit of two alternative contractual/ organizational forms in implementing the efficient outcome identified in the previous section, given the limitations on the contractual capabilities discussed previously. The alternatives are (a) either firm can set up a WS and employ the other firm as an `agent' whose compensation is linked to the subsidiary's profits, and (b) the two firms set up an equity joint venture where each has equity shares. 3.1. The wholly-owned subsidiary We first consider the case of a contract between a WS and its agent. We denote by (WS)1 a subsidiary wholly owned by Firm 1, with Firm 2 its agent, and by (WS)2 a subsidiary wholly owned by Firm 2, with Firm 1 its agent. In the case of (WS)1, the ~ contract offered by Firm 1 to its agent Firm 2 can take the general form of {, P12, K}, 11 where  is the fraction of the subsidiary's verifiable profits retained by Firm 1, P12 denotes a lump-sum transfer made by Firm 1 to Firm 2 conditional on V being realized, ~ is an ex ante lump-sum transfer that is made by Firm 2 to Firm 1 irrespective of the and K project outcome. In what follows, we show that given non-contractibility of the future 10 In principle, the two firms could write the following contract: Firm 1 and Firm 2 get X and R-X, respectively, if the project is successful; otherwise, each party pays a huge penalty to a third party. Given risk neutrality, this contract can induce first-best efforts from the two firms. However, if there is some small exogenous probability  of project failure [e.g., (e1, e2) ˆ e1 e2 ÿ ], and if the firms have limited liability (or equivalently, their utilities are minus infinity if their payoffs are negative), then such a contract is infeasible, and only the second-best outcome can be obtained. Note that, even if exogenous probability of project failure and limited liability are introduced into our model, the main results would still go through by setting Y ˆ 0. 11 Throughout, we denote by  the profit or equity share for Firm 1 ± as the case may be ± and 1- that for Firm 2.

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benefits, to implement the efficient allocation Z*, a large payment P12 contingent on V being realized may be necessary. However, in the presence of such a large payment, the owner of the subsidiary may abandon the project (even when it is successful) if at t ˆ 1 he observes the future benefits to be zero, which occurs with probability e1e2(1 ÿ 1)(1 ÿ 2). This establishes the inefficiency of the WS. 3.1.1. Profit sharing and ex post bargaining By assumption, the profits V from the targeted products are verifiable. Thus, Firm 1 and Firm 2 get respectively V and (1 ÿ )V. It remains to specify how the exclusive benefits, which are unverifiable, are shared. Notice that since these benefits (profits) are realized in the partners' own lines of business and not in the subsidiary, they cannot be automatically shared in the same way that V is shared, i.e., in the proportion  and 1 ÿ . Moreover, the courts are assumed not to be able to verify the realization of these benefits in the partners' own lines of business, so other rules for sharing these exclusive benefits are also ruled out. We also rule out blanket agreements of the following kind: the firms agree that they can use any unforeseen patents that are attributable to the joint R&D activity by making pre-specified transfers to the subsidiary. A fixed ex ante price agreement of this nature could subject the firms to the same problems that are associated with fixed-price contracts in an uncertain environment. For example, suppose (WS)1 is formed, and Firm 2 is found to have exclusive net benefits S2. Development of the previously unforeseen product typically will involve some costs for the subsidiary. Because these costs are unforeseen as well, it is possible that these costs exceed the previously agreed upon fixed price. In this case, it is not optimal for Firm 1 to agree to the development of the product. Thus, it would be inefficient for Firm 1 to commit not to renegotiate.12 It follows that there will be interim bargaining between the two parties regarding the sharing of the exclusive benefits. In this section, we assume that all the ex post bargaining power is with the owner of the subsidiary. This assumption will be relaxed in Section 4, but for now, it will prove very useful in bringing out the main ideas. Formally, we assume that this ex post bargaining power is reflected in the owner making a take-or-leave price offer (which we refer to as the transfer price), which the agent has to pay to the subsidiary for the right to use the unforeseen products of the venture.13 Notice, however, that we do not allow interim bargaining at t ˆ 1 over V, i.e., the original agreements contingent on success are not renegotiated. To give the owner all the bargaining power at this stage would completely destroy effort incentives for the agent, because we shall see below that the agent gets none of the exclusive benefits either. Since

12 While we do not model the costs of product development explicitly, we may assume that the payment made by a firm to the subsidiary consists of two parts: a payment covering the cost, plus a share of the surplus, where the surplus is net of the development costs. With the surplus defined in this way, our analysis would be completely unchanged. It is apparent that inefficiency could also arise if the realization of the exclusive benefits S2 conditional on the success of the project was a random variable drawn from some continuous distribution, since with a fixed-price contract, trade would not occur for all realizations of S2. 13 There is also an issue here of ownership of the innovation. We assume that the ownership belongs to the subsidiary. None of the results would change if ownership belonged to the owner of the subsidiary.

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this is obviously not a desirable outcome for the owner, we assume that the owner, in essence, can make a binding commitment at t ˆ 0 not to renegotiate the initial contract.14 Thus, to summarize, given the contractual limitations, the compensation to Firm 2 in the event of (WS)1 being formed can be specified as a fraction of the subsidiary's verifiable profits, denoted by 1 ÿ , and a payment P12 conditional on V being realized. Notice that profits of the subsidiary include V as well as any payments made by Firm 2 for unforeseen products.15 The following is immediate from the assumptions made regarding ex post bargaining power: Lemma 2. If (WS)1 is formed, Firm 1 captures all of Firm 2's exclusive benefits from unforeseen products. A corresponding result holds for (WS)2. Proof. Since Firm 1 has all the bargaining power, it can make a take-or-leave offer T ˆ (S2/). If Firm 2 accepts, its payoff is (1 ÿ )T ÿ T ‡ S2 ˆ 0. Thus, Firm 2 accepts and breaks even, while Firm 1 gets T ˆ S2. & 3.1.2. The possibility of project abandonment We now show that as a consequence of Lemma 2 and the assumed information structure, the second-best outcome as identified in Lemma 1 cannot always be implemented either by (WS)1 or by (WS)2. Consider (WS)1. Observe first that the expected payoff to Firm 2 conditional on V being realized, given Lemma 2, is P12 ‡ (1 ÿ )V, since Firm 2 does not get any part of its exclusive benefits. Fix any payment (from Firm 2 to Firm 1) conditional on the project being declared a failure at t ˆ 2, Y. Suppose that P12 ‡ (1 ÿ )V ‡ Y > V (which implies V ÿ P12 < Y), and consider the case where, at t ˆ 1, Firm 1 observes that the project of the targeted products is successful (which happens with probability e1e2) and that both exclusive benefits are zero (which happens with probability (1 ÿ 1)(1 ÿ 2) conditional on the success of the project). Now, continuing with the project would imply a payoff of V ÿ P12 for Firm 1, whereas causing the project to fail would imply a payoff of Y for Firm 1. Thus, in such cases, the project would be declared a failure, i.e., the ex ante probability of the project being implemented would be less than ^e1^e2 . An analogous argument establishes that in the case of Firm 2 setting up a WS and offering a contract to Firm 1, if P21 ‡ V ÿ Y > V (where P21 denotes a payment from Firm 2 to Firm 1 contingent on V being realized), then a successful project will be abandoned with probability (1 ÿ 1)(1 ÿ 2). We have the following: Proposition 1. No WS can implement the second-best efficient outcome characterized in Lemma 1 if both of the following conditions hold: 1 ÿ Z  > V;

(5)



Z > V: *

*

(6) *

Proof. (i) 1 ÿ Z > V implies (1 ÿ X ) ‡ Y > V. Recall that 1 ÿ X is the expected payoff to Firm 2 conditional on success. Thus, we need to set P12 ‡ (1 ÿ )V ˆ 1 ÿ X*. 14 For example, the owner posts a bond that is forfeited if it can be proved that the owner tried to renegotiate the contract. 15 The owner does not need to pay for the unforeseen products.

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However, we saw above that P12 and  with P12 ‡ (1 ÿ )V ‡ Y > V will cause failure with probability (1 ÿ 1)(1 ÿ 2), and hence (WS)1 cannot implement the second-best outcome. (ii) Next consider Z* > V. This implies X* ÿ Y > V, where X* is the expected payoff to Firm 1 conditional on success. Thus, we need to set X* ˆ P21 ‡ V. However, we again saw above that P21 and  with P21 ‡ V ÿ Y > V will cause failure with probability (1 ÿ 1)(1 ÿ 2), and hence (WS)2 cannot implement the second-best outcome. & Notice that a necessary condition for Eqs. (5) and (6) to hold is 1 ÿ V > V, i.e., V1 ‡ V2 > V. Thus, only if the non-contractible future benefits are sufficiently high will a WS fail to implement the second-best outcome. Intuitively, an agent under a WS, even though it has a profit-sharing contract, gets none of its own exclusive benefits. Hence (assuming w.l.o.g. Y ˆ 0), for the owner of the subsidiary not to abandon the project when both exclusive benefits are zero, the most that can be promised to the agent contingent on V being realized is in fact V. This implies that whenever the optimal success-contingent payments Z* and 1 ÿ Z* both exceed V, the second-best outcome cannot be implemented. In the next subsection, we shall see how, even in the absence of verifiability of exclusive benefits, an EJV can achieve a sharing of these benefits and thus attain the second-best outcome. 3.2. Equity Joint Venture 3.2.1. Equity shares versus profit shares Suppose firms 1 and 2 set up an EJV. Both firms receive equity shares, as distinguished from profit shares. Equity shares differ from profit shares because they are associated with certain rights that shareholders have. These rights will be discussed below. First, shares of equity may be associated with voting rights. Not all classes of equity need be associated with voting rights, however. The fact that both voting and non-voting shares may exist gives the EJV considerable flexibility, as will be seen below.16 Second, equity shares are associated with shares of profit. This right, of course, also exists in the case of a WS offering a profit-sharing scheme to an agent. Most importantly for our purposes, equity is associated with marketability. When the joint venture is a separately incorporated entity, as is often the case, the partners are issued equity share certificates that are transferable to third parties.17 When the joint 16 However, our main results do not depend on the possibility of two classes of shares. In fact, restricting attention to voting shares only enriches the analysis. See Section 3.2.4. 17 Sometimes, however, restrictions are imposed on transferability: the most common form of restrictions being that the partner has the `right of first refusal'. In practice, this means that if a party wants to sell its share to outsiders, it must make a first offer to its partner/partners by picking a price and specifying the quantity of shares being offered for sale. Two restrictions apply: if the offer is refused, ``the selling party shall not sell such shares to any third party at (a) a lower price than the price at which such shares were offered to the offeree party and/or its designee and (b) on other terms or conditions more favorable than those offered to the offeree party or its designee'' (See The Practical Guide to Joint Ventures and Corporate Alliances, by Robert Porter Lynch, 1989, Appendix C.). Thus, while the `right of first refusal' may be introduced into the joint venture agreement to prevent a hold-up problem associated with the transfer of shares to undesirable third parties, there seems little doubt that the shares can be sold at `market value' if needed.

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venture is organized as a partnership, the restrictions on transferability to third parties are at times more severe. However, ``...[a] partner's interest is a personal property interest that belongs to the partner. It can be sold (transferred) or pledged as collateral to a creditor.''18 Moreover, it is also quite common for the partnership agreement to stipulate that a partner can sell its interest to the other partners at `fair market value'(determined by independent appraisers, or through arbitration). This also imparts a feature of marketability to the partner's shares. In summary, both the partner in a joint venture and the agent in a contract are bound by an agreement to provide services such as technical training, availability of know-how, etc. (aside from the unverifiable resource contributions essential for the success of the project that we have called `effort'). In the case of a joint venture, the profit shares can be dissociated from the agreement and transferred: they are recognized as rights that are alienable from the agreement and entitled to fair compensation when sold. No such rights, however, exist for the compensation contract for the agent. The agent has no right to sell the contract ± either to the employer firm or to a third party ± and receive `fair market value'.19 3.2.2. The optimality of EJVs Before we come to interim bargaining and the issue of how marketability matters, we need to specify our assumptions about ex post bargaining power. In the case of the WS, there is a single owner, who, we assume, has all the ex post bargaining power. We now assume that for the EJV, the ex post bargaining power resides with the majority partner of the EJV ± the majority partner being defined as the partner with a majority of voting shares. While this assumption is made mainly for expositional simplicity, it may well capture the effects of the extreme asymmetry in decision-making power that comes about in a joint venture between majority and minority owners. The majority owner may be able to coerce the minority owner in many ways, such as investing in projects that benefit only the majority owner. The marketability of equity or agreements that enable a minority partner to sell their shares to the majority partner at fair market value (cf. Section 3.2.1) may resolve hold-up problems of this nature. In Section 4, we show that our results are robust to more general bargaining frameworks. To see how marketability matters for the interim bargaining, suppose that Firm 1 owns a fraction a of all shares, and has majority voting shares. Firm 2 has been revealed to have exclusive benefits of S2 from an unforeseen product. At issue is the division of these benefits, under the assumption that Firm 1 has all the bargaining power. For now, we shall assume that the realization of the exclusive benefit S2 is common knowledge, even though, as we have assumed, the realization of these exclusive benefits in Firm 2's other lines of business cannot be verified by a third party such as a court. 18 Business and the Legal Environment by Marianne Moody Jennings, 1991, page 521, second edition. Emphasis added. 19 Of course, in principle, the parent firm of the agent may be able to spin-off the contract from the rest of the company's assets and set up a new company, but this would be a costly way to market the profit shares. In any case, our purpose is to point out that marketability of profit shares is important in the presence of contractual incompleteness and that EJV has this feature. Why we do not observe contracts with the feature of marketability added on is, in some sense, a distinct issue.

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We assume the following sequence of moves. Firm 2 makes an offer to Firm 1 of a transfer price to be paid by Firm 2 to the EJV for the right to use the innovation. Firm 1 can accept or reject this offer. If Firm 1 rejects, Firm 2 can sell its equity to outsiders. After this, Firm 1 can make a take-or-leave offer.20 We assume that selling equity to outsiders involves a small cost of ". We show that in equilibrium, Firm 2 will offer to pay a transfer price of T ˆ S2 for the use of the innovation to the EJV, and Firm 1 will accept. It is important to understand the off-equilibrium payoffs if Firm 1 rejected the offer. Then Firm 2 could sell off its entire equity for a price  ± where  is derived from the following consideration. Given that Firm 2 has sold its share and it is Firm 1's turn to move, Firm 1 makes a take-or-leave offer of the right to the innovation to Firm 2 for a transfer price of S2 to be paid to the EJV. This offer leaves Firm 2 with zero profits and it will be accepted, and this is also the best offer from Firm 1's point of view, and Firm 1's overall payoff is (V ‡ S2). Given this, the new equity holders who bought Firm 2's shares will receive (1 ÿ a)(V ‡ S2). Thus, they are willing to pay  ˆ (1 ÿ )(V ‡ S2) for the equity. Hence, Firm 2 gets (1 ÿ )(V ‡ S2) ÿ " if Firm 1 rejects its offer, and Firm 1 gets (V ‡ S2) by rejecting Firm 2's offer. Now consider the proposed equilibrium offer by Firm 2. The payoff to Firm 1 from accepting this offer is (V ‡ T) ˆ (V ‡ S2). Thus, accepting the offer gives Firm 1 the same payoff as it can get from rejecting the offer, and so in equilibrium the offer will be accepted. The payoff to Firm 2, if this offer is accepted, is (1 ÿ )(V ‡ T) ‡ S2 ÿ T ˆ (1 ÿ )(V ‡ S2), which is " more than the payoff if the offer is rejected. Since any lower offer will be rejected, and acceptance gives " more payoff to Firm 2 than rejection does, it is optimal for Firm 2 to make such an offer. Consider now the division of Firm 1's exclusive benefit, S1. Firm 1 will make a take-orleave offer to buy the right to the innovation from the EJV by paying zero, which will be accepted by the Firm 2. It is also clear that the outcome will not change if Firm 2 sold its shares to outsiders. Thus, in this case, Firm 1 will get its entire private benefit, and Firm 2 will get nothing. Consequently, the total payoff to Firm 1 contingent on the success of the project is V1 ‡ (V ‡ V2) and that to Firm 2 is (1 ÿ )(V ‡ V2). Notice that since we allow for both voting and non-voting shares, the fraction of voting shares with Firm 1 can remain greater than 50 percent (e.g., Firm 2 could be given only non-voting shares, and Firm 1 retains a single voting share) but  could range from almost zero percent to 100 percent. Thus, when Firm 1 has majority voting shares, its payoff ranges from V1 (corresponding to  ˆ 0) to 1 (corresponding to  ˆ 1). An analysis exactly similar to the above shows that when Firm 1 has minority voting shares, its payoff ranges from 0 to V ‡ V1. Since V ‡ V1 > V1, any Z* 2 (0,1) (as identified in Lemma 1) can be supported by setting Y ˆ 0 and a suitable a, with one of the two firms having majority voting shares. It is important to note that since no direct transfer conditional on success (i.e., P12 or P21) is needed and Y ˆ 0, continuation can only be beneficial and there is no reason for either firm to cause the project to fail after the potential value of Si is observed. Thus, we have the following: 20 As will be seen below, the particular sequence of moves assumed implies that Firm 2 will not sell its equity in equilibrium. Alternatively, we could assume that Firm 1 makes the first offer, but Firm 2 can sell its equity before the offer is made. This would imply that Firm 2, in equilibrium, will sell all its equity to outsiders. Our main results do not depend on the specific sequences of moves.

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Proposition 2. An EJV that can issue both voting and non-voting shares can achieve the second-best outcome. In contrast to the case of WS, a minority shareholder under an EJV can secure a certain fraction of its own exclusive benefits. This, in combination with the flexibility of voting and non-voting equity, offers the two parties all possible contingent payoffs (i.e., Z* as identified in Lemma 1 can be attained), thereby requiring neither penalty for failure (Y ˆ 0) nor the lump-sum payment contingent on V(P12 ˆ P21 ˆ 0). The optimality of EJV over WS follows immediately. To summarize, the very nature of innovative activity creates a problem of knowledge appropriation and the sharing of the profits from the innovative activity. Since completely state-contingent contracts are not possible in this environment, ex post bargaining is inevitable. It is well known that bargaining, or the possibility of `hold up' in the terminology of Williamson (1975, 1985)), leads to suboptimal effort or investment choices. A feature of equity that helps mitigate this hold-up problem is its marketability. Marketability implies that profit shares are alienable from the rest of the joint venture agreement. It is this alienability that makes an EJV superior to a contractual arrangement, which entitles an agent to only a share of profits. The resolution of the hold-up problem we propose is thus in sharp contrast to the existing literature, which focuses on revelation mechanisms and/or renegotiation processes. The importance of alienability has been stressed by Jensen and Meckling (1992), who argue that ownership is meaningless without the right of alienability. In our analysis, it is precisely the feature of alienability that confers an ownership right to the equity holder. Jensen and Meckling argue that alienability is important in (i) colocating knowledge and decision rights, and (ii) providing the right incentives to decision makers. Our analysis further elaborates on these roles of alienability in the context of equity joint ventures. 3.2.3. Discussion Our explanation of the superiority of equity over contractual profit shares has stressed the ability of the minority shareholder to sell its ownership stake. We now argue that the ability to buy back the equity shares ± or give the buyers of the equity shares a sell-back option ± may also be important in situations where there may be some limitations on the marketability of equity, or in environments where weaker informational assumptions about the magnitudes of the private benefits than we have made are appropriate. The sellback option consists of a guarantee by Firm 2 to buy back the 1 ÿ  fraction of the shares at a total price of (1 ÿ )(V ‡ S2). Essentially, such a sell-back option gives some commitment power to the minority shareholder and thus restores some of the bargaining disadvantage. (1) Suppose Firm 2 can only sell its shares to a single outside party. Suppose also that Firm 1 can offer the product to the same third party for a price of T ˆ S2/, and commit not to offer the product to anybody else (including Firm 2) if the offer is rejected by the third party. In the absence of the sell-back option, the offer would be accepted because the third party, by reselling the product to Firm 2 for S 2 , would make S2 ‡ (1 ÿ )T ÿ T ˆ 0, which is the same as it gets by not accepting. In this case,  ˆ (1 ÿ )V. However, if the sell-back option is there, then this threat by Firm 1 is

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undone because now the third party, by rejecting Firm 1's offer, can always get (1 ÿ )(V ‡ S2) by selling the shares back to Firm 2. Thus, Firm 1's offer will be rejected by the third party, and knowing this, Firm 1 will not make the offer.21 (2) Absent any sell-back option, in the event that Firm 2 sells off its shares to outsiders, it would be optimal for Firm 1 and Firm 2 to strike a deal, whereby the ownership of the innovation will be with either firm, but not the EJV. This will deprive the new shareholders of the profits from the innovation, and Firm 2 will not be able to sell the shares for a price of  ˆ (1 ÿ )(V ‡ S2). However, if the sell-back option is present, it is not in Firm 2's interest to strike a deal which gives Firm 1 more than S2.22 (3) We have assumed that the realization of the exclusive benefits S2 is common knowledge: in particular, this is known to the new minority shareholder(s). We could, however, dispense with the assumption of observability of future benefits, so long as the sell- back option is there and the transfer payments are observable. Then, if the sell-back price is (1 ÿ )(V ‡ S2), the third party will sell back the shares if the transfer payments are less than S2 (i.e., the exclusive benefit of Firm 2 is zero). This implies that the shares can be sold for  ˆ (1 ÿ )(V ‡ S2), since the third party pays a fair price if the realization of exclusive benefits happens to be S2 and can avoid losses if the realization is zero. In equilibrium, Firm 2 will sell shares if and only if S2 is realized. 3.2.4. 50±50 joint ventures One potential objection to our analysis above is the following. Much of the power of the EJV seems to come from the assumption that the EJV can issue two classes of shares. As a matter of practice, though, it appears that deviation from the one-share-one-vote norm is relatively uncommon for EJVs.23 The inefficiencies associated with departures from the one-share-one-vote principle for public firms (see Harris and Raviv (1988) and Grossman and Hart (1988)) may in fact apply with even more force to joint ventures. For example, suppose an outside party is less efficient than the majority partner, but will enjoy private benefits from controlling the joint venture. If the partner with a majority of voting shares has a relatively small share of profits, the cost to the outside party from acquiring the majority voting shares will be small. This will encourage the inefficient outsider to gain control of the joint venture, purely for the sake of private benefits. In view of this, it may be important to see how our results are affected if attention is restricted to a single class of shares. We find that our major conclusions regarding the superiority of EJVs over contractual arrangements are not changed. In fact, one interesting implication of the one-share-one-vote restriction in our analysis is that we are 21 Notice that if Firm 2 could sell the shares to a large number of outsiders, it could ensure  ˆ (1 ÿ )(V ‡ S2) even without the sell back option. The price that any one of the new shareholders is willing to pay for the right to resell is decreasing in its share of the joint venture profits, and, in the limit as the number of such shareholders becomes very large, it is S2. 22 Alternatively, to the extent that it could be proved to a court that the new innovations are derived from knowledge generated in course of the pursuit of the targeted ones that are the property of the EJV, it could be argued that such practices would constitute `fraud on minority' and can be prevented by the minority shareholders. 23 Studies of equity joint ventures in China suggest that the one-share-one-vote restriction is in practice, see Pearson (1991).

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able to explain why certain forms of joint ventures, such as the so-called 50±50 or 51±49 equity joint ventures, are more commonly observed than others.24 The basic intuition for this comes from the assumption that the bargaining power over future benefits changes discontinuously as ownership changes from above 50 percent to below 50 percent.25 This also implies that payoffs change discontinuously. As a consequence, there is a range of possible values of Z* that cannot be exactly attained by any particular equity sharing arrangement; however, the payoffs corresponding to the 51± 49 or 50±50 EJVs are the `closest', so that these are optimal (`third-best') arrangements. Since these particular equity sharing arrangements are optimal for a range of values of Z*, we should expect to see such arrangements with positive probability, but any other equity sharing arrangement should have zero probability of being observed.26 3.2.5. Payoffs under a one-share-one-vote restriction When all shares are voting shares, a majority partner's share must be greater than 0.5, and that of the minority partner must be less than 0.5. While, as shown above, the share of the exclusive benefits received by each party is necessarily linked to its ownership, we do not assume such a link for the share of V going to a party ± allowing for lump-sum transfers conditional on success. However, considerations similar to those underlying Proposition 1 tell us that if Firm 1's payoff ± excluding its share of V1 and V2 ± is more than V conditional on the success of the project, then Firm 2 might cause the project to fail in some instances. Similarly, Firm 1 might cause the project to fail in some instances if it receives less than zero conditional on the success of the project. In such a case, the second-best outcome cannot be achieved. Hence, we assume that excluding its share of the exclusive benefits, Firm 1 gets a maximum of V and a minimum of zero. Thus, if Firm 1 is the majority partner, its share of exclusive benefits is V1 ‡ V2, where  > (1/2), and it can additionally receive anything between zero and V, if the project is successful. Thus, its overall payoff conditional on success of the project will span the interval ((1/2)V2 ‡ V1, 1]. On the other hand, if it is the minority partner, its share of the exclusive benefits is V1, where  < (1/2), and additionally, it can get anything from zero to V, so that its payoff will span the interval [0, (1/2)V1 ‡ V). Thus, if (1/2)V1 ‡ V > (1/2)V2 ‡ V1, which requires V > (1/2)(V1 ‡ V2), Firm 1's payoff spans the unit interval, and any Z* (as identified in Lemma 1) can be implemented. In this case, even if V < V1 ‡ V2 holds, so that the conditions in Proposition 1 hold and a WS cannot implement the second-best outcome, an EJV will always do so. On the other hand, if V < (1/2)(V1 ‡ V2), there is an interval ((1/2)V1 ‡ V, (1/2)V2 ‡ V1) that is not spanned, and the second-best outcome cannot be implemented by an EJV. Obviously, a WS cannot implement the second-best outcome either. It is for Z* in 24 See Pearson (1991) for evidence from the Sino-foreign joint ventures. Bleeke and Ernst (1991) also document the prevalence of the 50±50 joint ventures in their study of alliances among 150 top companies ranked by market value (50 each from United States, Europe, and Japan). 25 As we argued previously, for the one-share-one-vote setting, this is a natural assumption to make. The majority partner has the residual rights of decision making over events that cannot be foreseen ex ante, including the transfer prices to be set for unforeseen products. 26 The optimal Z* is a function of the model parameters. If we imagine that the model parameters are random draws from some distribution, a particular  will be optimal over a set of parameters of positive measure in our model - i.e., be observed with positive probability - only if it is optimal for a range of Z*.

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this range that the prevalence of the so-called 50±50 or 51±49 joint ventures will be observed. To see this, we first need to determine the payoff to Firm 1 in a 50±50 joint venture. Since neither party has the majority, some assumptions have to be made regarding bargaining power. If we assume that the parties have identical bargaining power in this case, then the share of exclusive benefits going to Firm 1 is (1/2)(V1 ‡ V2). Notice that the maximum payoff to Firm 1 as a 50±50 partner is V ‡ (1/2)(V1 ‡ V2), and the minimum payoff is (1/2)(V1 ‡ V2). We distinguish between two cases: Case 1 ( V  max f…1=2†V1 ; …1=2†V2 g). In this case, the maximum payoff from the 50± 50 arrangement to Firm 1 exceeds the minimum payoff when Firm 1 is a 51 percent majority partner, and the minimum payoff under the 50±50 arrangement is less than the maximum payoff when Firm 1 is a 49 percent minority partner. Thus, the entire unit interval can be spanned, and the EJV can implement the second-best outcome. Case 2 (V < max f…1=2†V1 ; …1=2†V2 g). In this case, part of the interval (though not all) ((1/2)V1 ‡ V, (1/2)V2 ‡ V1) remains unspanned. Thus, the second-best outcome cannot always be implemented by EJV. First, suppose that V < min{(1/2)V1, (1/2)V2}. Then the range of payoffs from a 50±50 EJV, [(1/2)(V1 ‡ V2), V ‡ (1/2)(V1 ‡ V2)], is a proper subset of the interval [(1/2)V1 ‡ V, (1/2)V2 ‡ V1]. Therefore, for Z* in the range of [(1/2)(V1 ‡ V2), V ‡ (1/2)(V1 ‡ V2)], a 50±50 EJV will once again implement the second-best outcome. For Z* in the complement of this interval in [(1/2)V1 ‡ V, (1/2)V2 ‡ V1], either a 50±50 or a 51±49 EJV (the latter with either Firm 1 or Firm 2 as the majority partner) will emerge as a `thirdbest' efficient outcome. Notice that since Z* in this case cannot be attained exactly, and under a WS1 and WS2 combined, the unspanned range is [V, V1 ‡ V2], one can always attain a payoff closer to Z* from either a 50±50, or a 51±49 EJV than a WS. Since the joint surplus P(Z) is concave in the payment conditional on success Z (as shown in the proof of Lemma 1), either a 50±50 or a 51±49 EJV will dominate a WS. Next, suppose that min {(1/2)V1, (1/2)V2} > V. Now, once again, a subset (though not a proper subset in this case) of the interval [(1/2)V1 ‡ V, (1/2)V2 ‡ V1] will be spanned by a 50±50 EJV. For Z* in the complement of that subset, either a 50±50 or a 51±49 EJV will again emerge as a third-best outcome. It is worth emphasizing once again that in all cases in which a 50±50 or a 51±49 EJV is optimal, they are optimal over a range of Z*. In contrast, any other ownership share is uniquely associated with a particular Z*. If we assume that the optimal Z* is drawn from an empirical distribution induced by randomly drawn model parameters, then this amounts to saying that 50±50 or 51±49 EJVs will be observed with positive probability, whereas any other EJV arrangements will be observed with (almost) zero probability. We summarize this discussion in the following Proposition: Proposition 3. Suppose V < V1 ‡ V2. Then for Z* in the range of [V, V1 ‡ V2], a WS does not implement the second-best outcome. However, (i) If V > (1/2)(V1 ‡ V2), the EJV always implements the second-best outcome.

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(ii) If V < (1/2)(V1 ‡ V2) but V  max {(1/2)V1, (1/2)V2}, the EJV always implements second-best outcome, and 50±50 EJVs will be observed with positive probability. (iii) If V < (1/2)(V1 ‡ V2) and V < max {(1/2)V1, (1/2)V2}, the EJV will not always implement the second-best outcome. However, 50±50 or 51±49 EJVs will be observed with positive probability. Thus, once we assume that only voting shares can be issued, the optimality of EJV over WS remains while the property of the 50±50 or 51±49 EJVs being observed with nonzero probability emerges. It is also interesting to note that these 50±50 and 51±49 EJVs become optimal arrangements when the future non-contractible benefits are significantly large compared with the verifiable profits. 4. A more general bargaining framework Our analysis so far has been based on some strong assumptions about relative bargaining power. It may be asked to what extent the results are driven by the particular assumptions about ex post bargaining that have been made. It turns out that the results are not very sensitive to the assumptions at all. We consider an extension of the basic model to show this. We make the same assumptions about the information structure, project payoffs and contractual capabilities as in Section 2. However, we assume that interim bargaining follows the Rubinstein (1982) bargaining game, with the time interval between offers very small, so that each party gets one-half of the pie to be divided. The issue is, how does the ownership of equity affect the bargaining outcome? Aghion and Tirole (1994) address this issue and show that ownership does not affect the Rubinstein bargaining outcome at all. However, Aghion and Tirole do not consider the issue of ex post marketability of equity. Absent such marketability ± as in the case of a WS ± irrespective of what the profit share of the `agent' is, the agent gets exactly one-half of its own and also one-half of the other firm's benefit. However, when the equity is marketable, each firm has the threat of first selling its equity stake to outsiders and then bargaining with the other firm. The following proposition summarizes the payoffs to the partners from interim bargaining over exclusive benefits. Proposition 4. (i) Suppose firm i has a profit-sharing contract of i in WSj. If its exclusive benefit is Si, then both firm i and firm j get (1/2)Si. (ii) Suppose firm i owns i fraction of equity in the EJV. If its exclusive benefit is Si, the firm gets (1/2)(1 ‡ i)Si from the bargaining game, and firm j gets (1/2)(1 ÿ i)Si. Proof. Please see the appendix. The intuition for this result can be easily understood as follows. When firm i has a nontransferable profit-sharing contract of i, it is expected to get more payoff, which, however, makes it less patient and more ready to strike a deal. In fact, the profit-sharing contract does not have any effect on the bargaining outcome, as conjectured by Hart and

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Moore (1990) and found by Aghion and Tirole (1994). In contrast, when firm i has marketable equity shares, it can sell equity shares to outside shareholders before bargaining with firm j, thereby credibly putting aside the part of its payoff that derives from the equity shares. While firm i still gets (1/2)Si in its subsequent bargaining with firm j, it can also get (1/2)iSi from the outside shareholders. Compared with WS, the bargaining outcome under EJV has two distinguishing features. First, under EJV a firm gets more of its own exclusive benefit but less of the other firm's, whereas under WS each gets same fraction of its own exclusive benefit as that of the other firm's. Second, under an EJV a firms' payoff increases in its equity share, whereas under a WS a firm's payoff is independent of its profit-sharing contract. As will be shown below, it is these two features which make an EJV dominate a WS. Consider first a WS. By Proposition 4, irrespective of whether it is (WS)1 or (WS)2, Firm 1 gets (1/2)(V1 ‡ V2) expected exclusive benefits from the interim bargaining. Suppose that Firm 1 also has  fraction of the verifiable profits V, and that upon the success of the project (i.e., realization of V) Firm 1 needs to pay Firm 2 P12. As discussed in Section 3, when V ÿ P12 < 0,27 Firm 1 may choose to make the project fail with probability (1 ÿ 1)(1 ÿ 2). To avoid that, an upper limit on P12 needs to be imposed, i.e., V ÿ P12 > 0 is imposed, which implies that V ÿ P12 has a minimum of 0. Similarly, in order that Firm 2 does not cause the project to fail, (1 ÿ )V ‡ P12 > 0, which implies V ÿ P12 has a maximum of V. It follows that Firm 1's payoff spans the range of [(1/2)(V1 ‡ V2), (1/2)(V1 ‡ V2) ‡ V]. In the case of an EJV, Firm 1 gets (1/2)(1 ‡ )V1 ‡ (1/2)V2 expected exclusive benefits from the interim bargaining. In addition, Firm 1 has V verifiable profits upon the success of the project - even without success-contingent payments P12. Thus, the overall payoff to Firm 1 is (1/2)V1 ‡ [(1/2)V1 ‡ (1/2)V2 ‡ V]. This implies that under EJV Firm 1's payoff spans the range of [(1/2)V1, (1/2)V2 ‡ V1 ‡ V]. Thus, the range of payoffs that can be spanned under a WS is a subset of that under an EJV. Thus, we have: Proposition 5. Under the new scenario of our model, an EJV dominates a WS. It may be noted that the range of payoffs under the EJV does not span the entire unit interval, so the EJV will no longer always implement the second-best outcome. However, the range over which only the EJV implements the second-best outcome can be large compared to the range over which both the EJV and WS implement the second-best outcome. For example, for V1 ˆ V2 ˆ 0.4 and V ˆ 0.2, both implement the second-best outcome for Firm 1's optimal payoff in the range [0.4,0.6]. However, only the EJV implements the second-best outcome for Firm 1's payoff in the range [0.2, 0.4) and (0.6, 0.8].28 27 We assume without losing generality Y ˆ 0 (i.e., the payment from Firm 2 to Firm 1 upon the failure of the project is zero). 28 The optimality of an EJV over a WS can also be shown if we assume that the probability with which firm i0 s exclusive benefits are realized depends on a further unverifiable effort by firm i. It can be verified from Proposition 4 that by setting Firm 1's ownership proportion equal to (V2/(V1 ‡ V2)), each firm gets in expected value the same share of overall exclusive benefits as under a WS (i.e. ((V1 ‡ V2)/2)); however, each firm gets a larger share of its own exclusive benefit. This encourages greater effort provision for the development of the exclusive benefits. See Dasgupta and Tao (1996) for details.

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5. Conclusion We address in this paper two empirical issues noted by existing studies (see Footnotes): the importance of equity joint ventures as an organizational form for cooperative R&D activity, and the prevalence of the so-called 50±50 or 51±49 joint venture arrangements. There is a growing literature on the organizational structure for R&D cooperation. In recent years, R&D cooperation has become an increasingly important business strategy. The rationales for R&D cooperation vary from coordination of R&D efforts to pooling of complementary skills. The problem of R&D coordination in research joint ventures is studied by Gandal and Scotchmer (1993). In their patent-race model, each firm can do R&D on its own. The gain for a group of firms to set up an research joint venture is that they can delegate the R&D investment to the most capable firm. The authors show how, under imperfect information about the participating firms' research abilities, budgetbalancing mechanisms could be designed that achieve perfect R&D coordination. Other papers consider R&D cooperation as a way of pooling complementary skills, and our paper belongs to this class. The main obstacle for such cooperation is the free-rider problem associated with team production. Holmstrom (1982) makes a pioneering contribution by elaborating the conditions under which team production leads to the freerider problem. Subsequent research aims at finding ways to solve the the team production problem. Radner (1991) and Vislie (1994) show that the free-rider problem can be eliminated if the participating firm's efforts are complements or sufficiently different. Radner (1991) also discuss how repeated interaction may alleviate the free-rider problem. Another solution to the free-rider problem is to have additional contracting variables as discussed in Gandal and Scotchmer (1993) and Morasch (1995). This paper is mostly related to Morasch (1995) in that both papers compares contractual and ownership arrangements for cooperative R&D. Morasch's analysis is built upon the observation that contractual arrangements for R&D cooperation have the advantage of low transaction costs but the disadvantage of difficult effort supervision. It focuses on the performance of ex ante cross-licensing agreements and investigates the conditions under which royalty schemes induce efficient R&D efforts so that ex ante cross-licensing agreements dominate joint ventures. In contrast, this paper seeks to explore possible differences between equity ownership and contractual arrangements other than those in transaction costs and effort supervision. We take the position that the difference between joint ventures and contractual arrangements is due to the difference between equity shares and profit shares. We argue that equity shares are associated with the property of alienability, which, as has been argued by Jensen and Meckling (1992), confers an ownership right to the holder of equity shares. We show that ownership matters in the context of contractual incompleteness. While this is familiar from the analysis of Grossman and Hart (1986), the essential aspect of ownership that is relevant in their analysis is the `residual rights of decision making' that is associated with the ownership of an asset. Both analyses, however, stress the role of ownership in mitigating ex post hold-up problems. Joint R&D projects are a natural context in which contractual incompleteness can be expected to prevail. The nature of innovative activity creates knowledge spillovers, leading to the possibility of future cooperation between the parties, which are often

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difficult to foresee in advance. The division of the benefits of these unforeseen outcomes are thus subject to ex post bargaining. It is well known that ex post bargaining distorts ex ante effort incentives, and thus can lead to inefficiencies. Our main contribution in this paper has been to show how ownership of equity such as in an Equity Joint Venture can alleviate the hold-up problem created by ex post bargaining, in contrast to other contractual arrangements that involve profit sharing only. Acknowledgements We thank Yuk-Shee Chan, Leonard K. Cheng, Gregory Chow, Vidhan Goyal, Oliver Hart, Jean-Jacques Laffont, Ivan Png and Kunal Sengupta for helpful discussions. We also thank editor Richard H. Day and two anonymous referees whose comments have significantly improved the paper. Appendix Proof of Lemma 1. Firm 1 chooses Z to maximize its total payoff P…Z†  ^e1^e2 ÿ c1 …^e1 †ÿc2 …^e2 † subject to condition (1) and (2). The first-order condition is …@P…Z†=@Z† ˆ …@…^e1^e2 †=@Z† ÿ …@c1 …^e1 †=@Z† ÿ …@c2 …^e2 †=@Z† ˆ 0. It can be shown that @c1 …^e1 † 1 Z 1 …1‡ 2 †=…1ÿ 1 2 † …1 ÿ Z†… 2 …1‡ 1 †=…1ÿ 1 2 ††ÿ1 ‰1 ÿ …1 ‡ 2 †ZŠ; ˆ …1 ÿ 1 2 † @Z @c2 …^e2 † 2 ˆ Z … 1 …1‡ 2 †=…1ÿ 1 2 ††ÿ1 …1 ÿ Z† 2 …1‡ 1 †=…1ÿ 1 2 † ‰ 1 ÿ …1 ‡ 1 †ZŠ; @Z …1 ÿ 1 2 † @…^e1^e2 † 1 ˆ Z … 1 …1‡ 2 †=…1ÿ 1 2 ††ÿ1 …1 ÿ Z†… 2 …1‡ 1 †=…1ÿ 1 2 ††ÿ1 @Z …1 ÿ 1 2 †  ‰ 1 …1 ‡ 2 †…1 ÿ Z† ÿ 2 …1 ‡ 1 †ZŠ: The first-order condition subsequently becomes @P…Z† 1 Z … 1 …1‡ 2 †=…1ÿ 1 2 ††ÿ1 …1 ÿ Z†… 2 …1‡ 1 †=…1ÿ 1 2 ††ÿ1 ˆ @Z …1 ÿ 1 2 †  ‰ 1 …1 ÿ Z†2 ÿ 2 Z 2 Š ˆ 0: There are three possible solutions to the first-order condition: Z ˆ 0 and Z ˆ 1 are ruled out for obvious reason. We are left with Z*, which satisfies  1=2 Z 1 ˆ : …1 ÿ Z  † 2 The second-order condition for Z* is met as the first-order derivative is positive for Z < Z* but negative for Z > Z*. Thus, P(Z) is higher if Z is closer to Z*, which is important for our analysis for Proposition 3. &

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Proof of Proposition 4. We model bargaining as an alternating-offer game (Rubinstein (1982)). Assume for simplicity of analysis that all parties have the same discount rate   eÿr
t where r is the instantaneous interest rate and
t is the time interval between successive offers. As standard in the strategic bargaining literature, there is a first-mover advantage which, however, vanishes when
t approaches zero. In what follows, we first present bargaining results assuming one of the parties is the first-mover and then summarize the limiting bargaining results when the time interval approaches zero. Case 1. Suppose that Firm 1 has realization of exclusive benefit (S1) whereas Firm 2 does not. Consider the bargaining between the two firms over S1. Assume that Firm 1 makes the first offer in the alternating-offer game. Before bargaining with Firm 2, Firm 1 has a choice of selling its equity shares to outside shareholders. (1) Suppose that, before bargaining with Firm 2, Firm 1 does not sell its share to outside shareholders. Following Shaked and Sutton (1984), assume that, in any subgame with Firm 1 making the first offer, Firm 1 gets M. If Firm 1 rejects Firm 2's offer made at t ˆ 1, it gets M at t ˆ 2. This implies that at t ˆ 1 Firm 2 needs to offer Firm 1 at least  M. Otherwise, Firm 2's offer will be rejected. Given that Firm 2 gets 1 ÿ  M at t ˆ 1, Firm 1 offers Firm 2 at least  (1 ÿ  M) at t ˆ 0. Otherwise, Firm 1's offer will be rejected. Thus, in the subgame starting at t ˆ 0 with Firm 1 making the first offer, Firm 1 gets 1 ÿ  (1 ÿ  M). Recall that, in any subgame with Firm 1 making the first offer, Firm 1 gets M. It follows that M ˆ 1 ÿ  (1 ÿ  M), which gives M ˆ (1/(1 ‡ )). When the time interval between successive offers approaches zero, then both firms get (1/2) fraction of S1. (2) Suppose that, before bargaining with Firm 2, Firm 1 sells its share to outside shareholders for a combined price of . The bargaining is still between Firm 1 and Firm 2; however, whatever the EJV gets will be divided among Firm 2 and the outside shareholders. As above, assume that, in any subgame with Firm 1 making the first offer, Firm 1 gets M. If Firm 1 rejects Firm 2's offer made at t ˆ 1, it gets M at t ˆ 2. It follows that at t ˆ 1 Firm 2 needs to offer Firm 1 at least  M. Otherwise its offer will be rejected. In this case, the EJV gets 1 ÿ  M, of which Firm 2 gets (1 ÿ )(1 ÿ  M). At t ˆ 0, Firm 1 needs to offer the EJV at least  (1 ÿ  M) of which Firm 2 gets (1 ÿ )  (1 ÿ  M). Otherwise its offer will be rejected. Thus, in the subgame starting at t ˆ 0 with Firm 1 making the first offer, Firm 1 gets 1 ÿ  (1 ÿ  M). It follows M ˆ 1 ÿ  (1 ÿ  M), which gives M ˆ (1/(1 ‡ )). When the time interval between successive offers approaches zero, both Firm 1 and the EJV get (1/2)S1. Note that, of the amount the EJV gets, Firm 2 has (1 ÿ ) fraction while the outside shareholders as a whole get  fraction. As this is expected ex ante, the outside shareholders are willing to pay a combined price of  ˆ (1/2)S1 when buying equity shares from Firm 1. As a result, Firm 1 gets a total payoff of (1/2)(1 ‡ )S1 while Firm 2 gets (1/2)(1 ÿ ) S1. Comparing Firm 1's payoffs under the two possibilities, it is obvious that Firm 1 chooses to sell its equity share before bargaining with Firm 2. Firm 1 and Firm 2 get respectively (1/2)(1 ‡ )S1 and (1/2)(1 ÿ )S1. Case 2. The case that Firm 2 has realization of exclusive benefit (S2) but Firm 1 has not can be analyzed similarly. Firm 2 chooses to sell its equity share before bargaining with Firm 1. Firm 1 and Firm 2 get respectively (1/2)S2 and (1/2)(2 ÿ )S2.

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Case 3. Suppose that both Firm 1 and Firm 2 have realization of exclusive benefits. Before bargaining, each of them has a choice of selling its equity to outside shareholders. (1) Suppose that neither sells its equity share before bargaining. Then, as similar to case 1(1), both firms get (1/2)(S1 ‡ S2). (2) Suppose that, before bargaining, Firm 1 sells its equity share to outside shareholders but Firm 2 does not. Now the EJV is owned by Firm 2 and the outside shareholders. The bargaining over S1 is similar to case 1(2); both Firm 1 and the EJV get (1/2)S1. On the other hand, the bargaining over S2 between Firm 2 and the outside shareholder is similar to case 1(1): both Firm 1 and the outside shareholders get a net payoff of (1/2)S2. As the outside shareholders get a total of (1/2)S1 ‡ (1/2)S2, they are willing to pay that amount ex ante when buying equity shares from Firm 1. As a result, Firm 1 gets (1/2)(1 ‡ ) S1 ‡ (1/2)S2 while Firm 2 gets (1/2)(1 ÿ ) S1 ‡ (1/2)S2. (3) Suppose that, before bargaining, Firm 2 sells its equity share to a large number of outside shareholders but Firm 1 does not. This case is similar to case 3(2). Firm 1 gets (1/ 2)S1 ‡ (1/2)S2 whereas Firm 2 gets (1/2)S1 ‡ (1/2)(2 ÿ )S2. (4) Suppose that, before bargaining, each firm sells its equity share to outside shareholders. Now the EJV is owned by the outside shareholders who bought Firm 1's share (called O1) and those who bought Firm 2's share (called O2). The bargaining between Firm 1 and the EJV over S1 is similar to case 1(2): both Firm 1 and the EJV get (1/2)S1. So too does the bargaining between Firm 2 and the EJV over S2: both Firm 2 and the EJV get (1/2)S2. As O1 gets (1/2)(S1 ‡ S2), Firm 1 has a total payoff of (1/2)(1 ‡ ) S1 ‡ (1/2)S2. As O2 gets (1/2)(1 ÿ )(S1 ‡ S2), Firm 2 has a total payoff of (1/ 2)(1 ÿ )S1 ‡ (1/2)(2 ÿ )S2. Comparing the firms' payoffs under the four possibilities, it is clear that, before bargaining, each firm chooses to sell its equity share to outside shareholders. Firm 1 gets (1/2)(1 ‡ )S1 ‡ (1/2)S2, while Firm 2 gets (1/2)(1 ÿ )S1 ‡ (1/2)(2 ÿ )S2. Finally, note that, upon the project being successful, Firm 1 can realize exclusive benefit S1 with probability 1, while Firm 2 can realize exclusive benefit S2 with probability 2. Thus, combining cases 1±3, we have the firms' expected bargaining payoffs that are summarized in Proposition 4. References Aghion, Philippe, Jean, Tirole, 1994. The management of innovation. Quarterly Journal of Economics 109, 1185±1209. Bleeke, Joel, Ernst, David, 1991. The way to win in cross-border alliances. Harvard Business Review 127±135. Bleeke, Joel and David Ernst, 1995. Is your strategic alliance really a sale? Harvard Business Review 97±105. Cohen, Jerome A., 1995. Going back for more. China Business Review 49±53. Dasgupta, Sudipto, Tao, Zhigang 1996. Contractual incompleteness, ownership rights and equity joint ventures. Manuscript, Hong Kong University of Science and Technology. Demski, Joel S., David, E.M. Sappington, 1991. Resolving double moral hazard problems with buyout agreements. Rand Journal of Economics 22, 232±240. Gandal, Neil, Suzanne, Scotchmer, 1993. Coordinating research through research joint ventures. Journal of Public Economics 51, 173±193. Gomes-Casseres, Benjamin, 1996, The Alliance Revolution: The New Shape of Business Rivalry. Harvard University Press.

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