Beyond asset ownership: Employment and assetless firms in the property rights theory of the firm

Journal of Economic Behavior & Organization 130 (2016) 261–273

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Beyond asset ownership: Employment and assetless firms in the property rights theory of the firm Leshui He 1 Department of Economics, Bates College, Pettengill Hall, Lewiston, ME 04240, United States

a r t i c l e

i n f o

Article history: Received 29 September 2015 Received in revised form 14 July 2016 Accepted 5 August 2016 Available online 8 August 2016 Keywords: Property rights theory of the firm Assetless firm Nexus of contracts

a b s t r a c t This paper enriches the celebrated Grossman–Hart–Moore (GHM) property rights model with employment relationships. By combining the GHM view of the firm as a bundle of asset ownerships with that of Alchian and Demsetz (1972), who viewed the firm as a nexus of contracts, the model yields, in some cases, optimal asset ownership different from the implications of the GHM model. We show that the nexus of contracts is a meaningful instrument to govern transactions even in the presence of asset ownership. The optimal contractual network structure depends on the relationship-specificity of investments, unlike the GHM model where the asset ownership depends solely on the asset specificity of investments. © 2016 Elsevier B.V. All rights reserved.

1. Introduction This paper analyzes a model that incorporates the well-celebrated property rights theory of the firm (Grossman and Hart, 1986; Hart and Moore, 1990; Hart, 1995) and the classical Alchian–Demsetz view of the firm as a nexus of contracts (Alchian and Demsetz, 1972). The dominant formal paradigm of Grossman, Hart, and Moore (GHM) sees the governance structure of the firm as arising from the optimal allocation of alienable assets, whereas the complementary view of Alchian and Demsetz (AD) considers the firm as a contractual network involving a team of players around one central player, who possesses the rights to “unilaterally terminate the membership of any of the other members without necessarily terminating the team itself or his association with the team.”2 Our combined model thus features implied employment relationships while inheriting the emphasis of GHM on the role of asset ownership in governing transactions facing ex ante incomplete contracts.

E-mail address: [email protected] I am deeply indebted to Professor Richard N. Langlois, my dissertation advisor, and Professor Robert Gibbons at the MIT Department of Economics and Sloan School of Management, my dissertation co-advisor. I would like to thank my advising committee members Vicki I. Knoblauch, Kathleen Segerson, and Christian Zimmermann for their helpful advice and suggestions. I would also like to thank Robert Akerlof, Ricardo Alonso, Daniel Barron, Joshua Gans, Ricard Gil, Henry Hansmann, Richard Holden, Hongyi Li, Desmond Lo, James Malcomson, Michael Powell, Michael Raith, Heikki Rantakari, Eric van den Steen, Giorgio Zanarone, Timothy Van Zandt, Birger Wernerfelt, and other participants of the MIT Organizational Economics Lunch Seminar Series for their comments. I am also grateful to Xenia Matschke, Xiaoming Li, and other seminar participants at the University of Connecticut, and seminar participants and discussants at ESNIE 2011 in Corsica and ISNIE 2014 at Duke University. I am grateful to the editor, Dr. Thomas Gresik, the associate editor, and two anonymous referees for their helpful insights. Any errors that remain are mine alone. 2 More specifically, Alchian and Demsetz (1972, p. 783) define the firm as “the contractual organization of inputs . . .with (a) joint input production, (b) several input owners, (c) one player who is common to all the contracts of the joint inputs, (d) who has rights to renegotiate any input’s contract independently of contracts with other input owners, (e) who holds the residual claim, and (f) who has the right to sell his central contractual residual status.” 1

http://dx.doi.org/10.1016/j.jebo.2016.08.003 0167-2681/© 2016 Elsevier B.V. All rights reserved.

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Formally, the nexus of contracts is added to the GHM framework by adopting the Myerson–Shapley bargaining solution, which considers the contractual networks as ex post bargaining networks. Because the GHM model implicitly assumes a complete bargaining network by adopting the Shapley value, this model encapsulates the standard GHM property rights theory of the firm when it models the contractual network explicitly as a part of the governance structure of the transaction. On the other hand, when the bargaining network is incomplete, a nexus of contracts arises. Similar to the notion of the residual control rights associated with asset ownership in the GHM framework, we refer to the control rights associated with the position of the nexus of contracts as the bargaining control rights over other players in the contractual network. This integrated model yields several novel results. The efficient governance structure may be to assign control rights of the nexus of contracts to the most important investor in the joint transaction while leaving asset ownership to others. One very instructive result of the model is that for the nexus of contracts to be optimal in any governance structure, at least one investor must make synergistic investments that enhance cooperation between the other players—that is, not only between the players and the investor herself. Examples of such synergistic investment could include mentoring, training, or investments in infrastructure undertaken to support other players’ cooperation. More generally, when the contractual network is taken into account, the optimal asset ownership can turn out to be different from what is prescribed in the classical GHM model without employment relationships, implying potential empirical opportunities to distinguish between these two theories. Two forces jointly drive the results in this model. When an investment is cooperative, more investment improves other players’ disagreement values and thus strengthens their bargaining positions. The investor is therefore discouraged to invest even if such investment is highly productive for the joint transaction. Incomplete contractual (bargaining) networks can improve investment incentives in such cases by placing that investor at the nexus position, limiting cooperative opportunities among other players, and thus reducing the adverse effects of her cooperative investment and improving her investment incentives. The second related force comes into play and changes the optimal asset ownership when it is optimal to use the nexus of contracts. When assets are the only instrument used to govern a transaction (i.e., a complete bargaining network), the optimal asset ownership solves the problem of balancing investment incentives. With the aid of an incomplete bargaining network, which alleviates some adverse effects from cooperative investments, asset ownership can be reallocated to further improve other players’ investment incentives, leading to asset ownership predictions that differ from the classical GHM model. The remainder of this article proceeds as follows. Section 2 reviews the relevant literature. Section 3 describes the setup of the model. Section 4 formally states and proves the analytical results. Section 5 further discusses the key modeling assumption used in the article to interpret bargaining control rights as a key characteristic of the firm beyond asset ownership. Section 6 concludes. 2. Related literature Our key modeling assumption of the bargaining control rights implied by the contractual network structure resembles exclusive rights in bargaining, which is a shared feature of several models in the literature. What sets the current model apart, however, is the feature of simultaneous allocation of asset ownership and bargaining control rights. Focusing the interpretation at the business unit level, Segal and Whinston (2000) characterize exclusive contracts as restricted bargaining rights in a seller–buyer relationship. They also emphasize the role of bargaining rights as an important instrument in the governance structure and discuss the conditions under which exclusive dealing is more efficient than non-integration. In particular, they find that if one trading player’s cooperative investment has a very high marginal product, it is efficient for her to control the other firm through an exclusive dealing contract. However, they do not explore whether exclusive dealing can still be efficient if the upstream firm can simply integrate with the downstream. In other words, can exclusive dealing be more efficient than both non-integration and full integration? If one interprets the incomplete bargaining network as exclusive dealing in our model, this article demonstrates that exclusive dealing can indeed be more efficient than both integration and non-integration. Second, we generalize their interpretation of bargaining networks beyond the exclusive dealing contracts to associate them with the employment relationship, which consequently provides an interpretation of assetless firms. In fact, one can consider the current article to be a generalization of Segal and Whinston (2000), adding asset allocation in incomplete bargaining networks. Rajan and Zingales (1998) provide another theory of the firm that does not rely on ownership of assets and one that sees the firm as a hierarchical structure. Assuming that the owner of the firm is fixed, Rajan and Zingales (1998) focus on the allocation of ex ante contractible access to the productive resource controlled by the owner. Those agents granted access become employees of the firm, and those who do not have access are interpreted as outsiders. The present article is different in several aspects. Most important of all, the major purposes of this model are to analyze alternative allocations of “critical resources” in terms of asset ownership or nexus of contracts. The “access” during renegotiation is an implied consequence of the contractual network. The current model shares the spirit of the subeconomy theory of the firm (Holmström and Milgrom, 1991; Holmström, 1999), where the firm can use various incentive instruments for their employees to selectively isolate them from external incentives offered by other firms. In Holmström and Milgrom (1991), the principal can choose a set of allowable tasks for the agent. In Holmström (1999), the firm can “regulate trade within a firm” as a subeconomy in the sense that the principal is able to set rules governing different activities of its agents, such as working from home. We do not study the problem from

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an agency-contracting approach, nor do we emphasize the information or measurement problem in organizations. Instead, we focus on a model in which the firm is able to regulate interactions between outsiders and its employees. One strand of the literature focuses on the GHM model with alternative bargaining solutions. Most importantly, Chiu (1998) and de Meza and Lockwood (1998) consider pairwise alternating-offer bargaining instead of the Shapley value used by GHM.3 These models focus on two-player cases; yet, the bargaining network design would be complete even for their cousin models with more players. The main purpose of their models is to evaluate the validity of the results obtained by GHM when the model adopts a different bargaining solution. In contrast, this article adopts a more general bargaining game to include GHM as a special case. The primary reason we use a generalized bargaining solution is to model an additional governance structure other than asset ownership. For this reason, this model is much closer to that of Segal and Whinston (2000) than the models of Chiu (1998) and de Meza and Lockwood (1998). de Fontenay and Gans (2005) and Kranton and Minehart (2000) study vertical integration and trade networks. In particular, de Fontenay and Gans (2005) adopt the GHM framework to compare outcomes under upstream competition and monopoly. Both these works and ours study integration, and both involve endogenous incomplete bargaining networks. The main difference is that we focus on analyzing governance structures in a fixed multilateral transaction that involves at least three players with asset allocation, whereas they consider governance structures across multiple bilateral transactions without asset allocation. Most importantly, the network in the current study’s model refers to status in the hierarchy. However, in de Fontenay and Gans (2005), the network refers to various transaction flows across different upstream sellers and downstream buyers.

3. Model setup This section describes the setup of the model. We follow Hart and Moore (1990) closely in our modeling choice to highlight the effects of bargaining control rights. Almost all the key modeling ingredients are identical to that provided in this seminal paper, except for the introduction of the bargaining network as a part of the governance structure affecting ex post bargaining results.

3.1. Economic environment Consider a joint transaction involving three players N = {1, 2, 3} whose main interest lies in the value of the final product or service.4 A pair of instruments, denoted by g = (A, B), govern their joint transaction, including asset ownership A and bargaining network B, which are specified later.

3.1.1. Timing Information is symmetric throughout the game. Players have sufficient wealth for transfer payments, so in equilibrium they will always implement the governance structure that maximizes joint surplus. This is a common assumption made in most of the literature on property rights framework. At t = 1, the players make ex ante non-contractible relationship-specific investments. At t = 1.5, the state of the world is realized. At t = 2, the players engage in efficient bargaining based on the governance structure, g = (A, B). Finally, at t = 3, the transaction is carried out, and the final value is produced and divided by the players according to the bargaining in stage 2.

As specified by the GHM model, the only inefficiency in this model arises from the ex ante investment stage. Because players maximize their individual returns from the bargaining instead of the joint return from the entire transaction, their investments differ from the first-best level (as shown later). The governance structure affects the efficiency of the transaction because the ex ante governance structure determines the ex post bargaining return of each individual, and thus induces different investment decisions ex ante. The most efficient governance structure is the one generating the highest level of final product net of the total private costs. Next, we discuss the assumptions and modeling choices in detail. Readers familiar with the GHM framework may skip directly to “bargaining under incomplete networks.”

3

The generalized Nash bargaining solution with equal bargaining power in the two-player case is a special case of the Shapley value. A model with three players is sufficient to capture all the key ingredients of the modeling framework. The model can be generalized to include more players. 4

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3.1.2. Investment At stage 1, each player i makes an ex ante non-contractible investment ei with private cost i (ei ).5 The investment cost i (ei ) is continuous, twice differentiable, increasing, and strictly convex in ei . Moreover, we assume  (0) = 0 and  (∞) =∞ to ensure interior solutions. We use e = (e1 , e2 , e3 ) to denote the vector of investments by all players. 3.1.3. Assets To produce the final output, the players need access to a set of alienable assets M. For simplicity, we analyze the model with only one, or sometimes two, assets. Asset ownership A(S) is a mapping from the set of players N to the set of assets M; specifically, A(S) ⊆ M denotes the set of assets under control of any coalition S ⊆ N. We discuss both sole player ownership and joint asset ownership in our analysis. 3.1.4. Production In stage 2, the players make production decisions based on (i) the realized state of the world and (ii) their control rights specified by the governance structure. These three players can potentially form different coalitions and reach agreements among themselves. Specifically, once an agreement is reached and implemented, coalition S ⊆ N can produce value vS . For instance, players 1 and 2 might reach an agreement without player 3 and choose their production decisions accordingly to maximize this value, denoted by v12 . For these three players, there are seven potential values in total, including the final value, v123 , produced under complete and full agreement from every player, and six status quo values, v12 , v13 , v23 , v1 , v2 , and v3 , that different combinations of players are able to produce without complete agreement. The value any coalition S can produce, vS (e, A), is determined jointly by the vector of ex ante investments e and asset ownership A(S). We allow vS (e, A) to benefit from investments of players outside S, a feature referred to as cooperative investment or cross investment in the literature.6 The cooperative investment increases the value that other players can obtain even when agreements cannot be reached with the investor herself.7 Following Hart and Moore (1990), we assume the production technology follows the following regularity conditions. (i) vS (e, A) is increasing, continuous, twice differentiable, and concave in investment ei for any S and A. Moreover, an empty coalition produces nothing, v∅ (e, A) = 0. (ii) Investments and assets are complements, that is, investments are asset-specific (Segal and Whinston, 2012). Specifically, ∂ vS (e, A) ≥ ∂ vS (e, A ) for A (S) ⊂ A(S). (iii) Investments are complementary in production, that is,

∂ei ∂ei ∂ v2 (e, A) ≥ 0 for any i, j. (iv) To make sure the problem is nontrivial, we assume that other things ∂ei ∂ej S

being equal, the value of production is superadditive. In other words, any two separate coalitions produce a smaller total value than they could if they were producing as a joint coalition.8 To simplify notations, whenever investment level e and asset ownership A are fixed, we write vS = vS (e, A). The bargaining structure we adopt ensures that the ex post renegotiation is always efficient. Therefore, under the abovementioned assumption (iv), only the grand coalition’s production v123 will be produced at the final stage. However, the distribution of the final output depends on the status quo. Moreover, to generalize the model to include both self and cooperative investments, we make one additional assumption. Assumption 1.

The investments are relationship-specific. More precisely, we assume, for any i, j, k ∈ N and any A,

∂vij (e,A) ∂v (e,A) ≥ j , ∂ej ∂ej ∂vik (e,A) ∂v (e,A) 2 (relationship-specific cooperative investment) ≥ k , ∂ej ∂ej ∂vijk (e,A) ∂vjk (e,A) ∂vijk (e,A) ∂v (e,A) ∂v (e,A) ≥ , and ≥ i + j . 3 (relationship-specific joint production) ∂ej ∂ej ∂ej ∂ej ∂ej

1 (relationship-specific self investment)

Assumption 1 guarantees that the marginal contributions of the other players are non-decreasing in player i’s investment.9 This fact consequently implies that investments generate positive externalities in other players’ bargaining payoffs (as shown later in Lemma 1), which then leads to the well-known result of under-investment in equilibrium in this area. Assumption

5 The investments take place ex ante in the sense that the state of the world has not been realized at the point of investment. They are non-contractible by the assumption that the investments are so complicated that they cannot be specified in a contract, nor can they be verified by any outside player, say, the court. 6 See for example, Che and Hausch (1999), Segal and Whinston (2000), and Whinston (2003). 7 The following two examples are provided in Che and Hausch (1999): (1) Nishiguchi (1994) p. 138 reports that suppliers “send engineers to work with automakers in design and production. They play innovative roles in. . .gathering information about the automakers’ long-term product strategies.” (2) After Honda chose Donnelly Corporation as its sole supplier of mirrors for its U.S.-manufactured cars, “Honda sent engineers swarming over the two Donnelly plants, scrutinizing the operations for kinks in the flow. Honda hopes Donnelly will reduce costs about 2% a year, with the two companies splitting the savings” (Magnet, 1994). 8 This is a somewhat restrictive assumption. If it does not hold, there is no benefit for these players to produce together, so the problem is no longer interesting. In fact, this is a maintained assumption in most of the literature on the property rights theory of the firm. 9 This assumption generalizes Assumption 6 in Hart and Moore (1990), which is equivalent to our assumption of the absence of cooperative investments, a possibility ruled out in their article.

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Fig. 1. Complete and incomplete bargaining networks for three players.

1 maintains an economic environment as close as possible to that specified by the GHM framework; thus, we can underline how bargaining control rights lead to different predictions in the optimal governance structure design. 3.1.5. Bargaining under incomplete networks At the ex post bargaining stage, each player is either one of two types depending on the bargaining network structure. A player is either restricted in bargaining—she needs consent from another player to implement any agreements with a third player—or the player is free in bargaining—she can freely implement decisions with other players. In a bargaining network, a player restricted in bargaining is connected with one and only one other player. A player free in bargaining is connected with the other two players. In a complete bargaining network, every player is free in bargaining, whereas in an incomplete bargaining network, the only player free in bargaining becomes a nexus. The requirement that each player has to be one of the abovementioned two types implies that the bargaining networks have to be connected.10 We use i : j to denote the link in a bargaining network between any two players i and j. A bargaining network is a set of links. For three players, there are four possible connected bargaining networks (Fig. 1). There is one complete network Bc = {i : j, i : k, j : k}, where any two players can freely reach agreements and implement them without restrictions. Moreover, there are three incomplete networks Bi = {i : j, i : k} for i = 1, 2, 3, where players j and k are only connected through player i. In these incomplete networks, player i is the nexus of contracts whose consent is necessary for the other two players to implement any renegotiated decisions on existing contracts. We say player i has bargaining control over player j if j needs i’s consent to implement any decisions with a third player. As a result of the incomplete network Bi , j and k cannot implement joint agreements to produce value vjk without player i.11 We apply the Myerson value (Myerson, 1977) to characterize the payoffs for each player from the joint production. Under the complete network, the bargaining payoff given by the Myerson value reduces to the original Shapley value payoff used in Hart and Moore (1990).12 This feature allows the current model to replicate the exact GHM model when the bargaining network is complete. Thus, we are able to compare the governance structures with incomplete bargaining networks, that is, with a nexus of contracts, side by side with the classical GHM structures represented by the complete bargaining network. Incomplete bargaining networks restrict the value that some sub-coalition S can produce when the players in S are not connected. For three players and four connected networks, the incomplete bargaining network Bi affects the bargaining payoffs by restricting the disagreement payoff for j and k together to only vj + vk , as opposed to vjk . For our purposes, this feature captures the idea that j and k cannot implement partial agreements without i’s consent when she has bargaining control rights. The rest of the bargaining solution is identical to those given by the Shapley value, and the specific bargaining payoffs are presented in the following section. 3.1.6. Governance structure Governance structure g = (A, B) has two parts. Asset ownership A describes who owns which assets. Bargaining network B restricts what agreements can be implemented. These two aspects jointly determine the bargaining payoffs of each player given investment level e. Given asset allocation A and ex ante investments e, bargaining payoff Yi for any player i is presented below for three different bargaining networks—the complete bargaining network Bc ; the incomplete bargaining network with player i as the nexus Bi ; and the incomplete bargaining network with another player j as the nexus Bj .13 Yic =

10

1 1 1 1 (v − vjk ) + (vij − vj ) + (vik − vk ) + vi ; 3 ijk 6 6 3

(1)

Because any player has to be connected with at least one other player, no player can be left isolated. If there exists an explicit contract providing bargaining rights between j and k without i, then the incomplete network Bi becomes essentially identical to the complete network Bc . Although arrangements explicitly permitting an employee to contract without consent from her boss are rare in reality, the opposite arrangement is quite common, such as non-compete clauses, which (possibly) renders Bc essentially incomplete. I thank one of the anonymous referees for pointing this out. 12 Myerson shows that this solution generalizes the Shapley value to bargaining in incomplete but connected networks, in two senses: (i) the Myerson value equals the Shapley value when the bargaining network is complete, and (ii) the Myerson value is the unique solution satisfying axioms akin to those that produce the Shapley value. 13 In a model with three players, it is sufficient to focus on three bargaining networks for any player i: the complete bargaining network; the incomplete network, where i is the nexus; and the incomplete network, where another player is the nexus. 11

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Yii =

1 1 1 1 (v − vj − vk ) + (vij − vj ) + (vik − vk ) + vi ; 3 ijk 6 6 3

(2)

j

1 1 1 1 (v − vjk ) + (vij − vj ) + (vi + vk − vk ) + vi . 3 ijk 6 6 3

(3)

Yi =

Following the literature, we make the following assumption related to the payoffs, which consequently implies that the game is supermodular.14 Assumption 2. Ex ante investments (ei , e−i ) are strategic complements in the investment game, that is, each player’s payoff Yi − i has increasing differences in (ei , e−i ), which, given the differentiability assumptions on Yi and i , is equivalent to ∂(Yi −i )2 ≥ 0 for any i, j.15 ∂ei ∂ej

Observation of the payoffs highlights the fact that the current model can be viewed as a combination of the GHM model with Segal and Whinston (2000), by jointly considering effects of both asset ownership A and bargaining network B as follows. As in the GHM model, asset ownership A directly determines the value of each specific vS but has no restriction on which vS are available. The standard GHM model uses the Shapley value in Eq. (1) to characterize the payoffs. Assuming a complete bargaining network with no restriction in ex post bargaining, all the sub-coalitional status quo vS are available. Also, because each production function vS (e, A) is a function of ex ante investments e and asset ownership A, the GHM model explores effects when A changes vS . As in Segal and Whinston (2000), the bargaining network B does not directly determine the values produced by each coalition, but instead dictates whether some sub-coalitional values, such as vjk , can be implemented, that is, which payoff function among Eqs. (1)–(3) determines player i’s bargaining payoff. The comparison of these three equations highlights the effect of bargaining networks. Under Bi , player i is the nexus. As a result, vjk is removed from the bargaining payoffs, that is, the other two players cannot implement joint production decisions without i. When player i is under the bargaining control of player j, not only does vik drop out, but player i’s payoff is no longer affected by vk . Notwithstanding differences in interpretation, Segal and Whinston (2000) analyzes the effects of the bargaining network B by comparing (1) with (2) and (3), assuming asset ownership A as fixed. The current model further analyzes the joint interactions of both A and B as instruments of governance structure design. 4. General results We first show that there is under-investment in equilibrium for all governance structures. Therefore, the governance structure that induces higher investments is more efficient. Next, we present a benchmark result showing that using the nexus of contracts (an incomplete bargaining network) is inefficient compared to the GHM model in the absence of cooperative investments, which constitutes a particular form of externality in investments. After establishing this benchmark, we present the key findings of this article. First, given fixed asset ownership, using bargaining control rights is more efficient when players make synergistic cooperative investments and self investments are only relationship-specific to some players. Second, we identify several conditions where the current model can yield different optimal asset ownership predictions compared to the GHM model. 4.1. Preliminaries Before specifying the ex ante investment problem under any governance structure, it is useful to pin down the first-best investment level as a benchmark. The first-best level of investment eiFB maximizes the final value of production v123 ; it is

thus characterized by ∂ v123 = i . ∂ei

Having established the benchmark, we characterize the ex ante investment levels eiA,Bc , eiA,Bi and ejA,Bi in the respective

Nash equilibria under different bargaining networks, given fixed asset ownership A.16

14 15

See, for example, Segal and Whinston (2012). Let j, k ∈ {1, . . ., K} be such that j = / k. Then a function f(zj , zk , z−jk ) has increasing differences in (zj , zk ) if, for all z−jk , all zjL , zjH ∈ Zj such that zjH > zjL ,

and for all zkL , zkH ∈ Zk such that zkH > zkL , we have

f (zjH , zkH , z−jk ) − f (zjL , zkH , z−jk ) ≥ f (zjH , zkL , z−jk ) − f (zjL , zkL , z−jk ). See more in, for example, Milgrom and Roberts (1990). In the current model, one sufficient condition assumption to hold is if the complementarity for this ∂ v2 (e, A) for any S, its partition {Sl }, and any i, in investments is non-increasing with respect to separation of any coalition, that is, ∂e ∂∂e v2S (e, A) ≥ ∂e ∂e S i

j

Sl

i

j

l

j. See the online Appendix for the proof of this claim. 16 The efficiency implications regarding the optimal asset ownership, given the free bargaining network Bc , are well known in the literature. See Segal and Whinston (2012) for an extensive survey.

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A,Bc , A) =  for each i, where Under Bc , player i obtains Yic ex post; thus, eiA,Bc is characterized by jointly solving ∂ Yic (ei , e−i i

A,Bc denotes equilibrium investments by other players. Yic is defined by Eq. (1), and e−i

Similarly, eiA,Bi , ejA,Bi , and ekA,Bi are characterized by solving

∂ Y i (e , eA,Bi , A) =  , respectively. k ∂ek k k −k

∂ei

∂ Y i (e , eA,Bi , A) =  , i ∂ei i i −i

∂ Y i (e , eA,Bi , A) =  , and j ∂ej j j −j

The proofs of the following lemmas can be found in the Appendix.

Lemma 1. Investments have non-negative externalities over other players’ bargaining payoffs, that is, each player’s bargaining payoff Yi is non-decreasing in other players’ investments e−i . The following lemma enables us to rank the efficiency of different governance structures by their corresponding equilibrium investment levels. Lemma 2. eiA,B

≤

eiFB

There is always under-investment in any bargaining network Bc , Bi , and Bj regardless of asset ownership. That is,

for any i and any (A, B). Therefore, a governance structure that induces higher equilibrium investments is more efficient.

4.2. Allocations of bargaining control rights in fixed asset ownership 4.2.1. Cooperative investment as a necessary condition for bargaining control rights Cooperative investment is a necessary condition for bargaining control rights to be efficient. The following proposition establishes this benchmark for our analysis. Proposition 1.

If there is no cooperative investment, that is, for all S ∈ / i,

∂vS = 0, then having bargaining control rights is ∂ei

inefficient; in other words, regardless of asset ownership, Bc is always more efficient.

Proof. The proof applies monotone comparative statics results to rank the equilibrium investment levels under different governance structures, which are consequently ranked by Lemma 2. Without loss of generality, we compare incomplete network Bi with complete network Bc , where ei and ec are their corresponding equilibrium investments. We define Yio (ei , e−i , A, ) =

⎧ ⎨ Yic

if  = 0

⎩ Y i = Y c + 1 (vjk − vj − vk ) if  = 1, i i

(4)

3

and Yjo (ej , e−j , A, ) =

⎧ ⎨ Yjc

if  = 0

⎩ Y i = Y c − 1 (vjk − vj − vk ) if  = 1. j j

(5)

6

This construction is the key to all the proofs in this paper and is similar for all the propositions that follow. The parameter  is constructed to indicate a family of different payoff functions in order to apply the monotone comparative results. In (4), when there is no cross investment, ∂ (vjk − vj − vk ) = 0; thus, Yio has (trivial) increasing differences in (−ei , ). ∂ei

Moreover, ∂ (vjk − vj − vk ) = ∂ (vjk − vj ) > 0 by Assumption 1. Thus, by (5), Yjo has increasing differences in (−ej , ). By ∂ej

∂ej

Assumption 2, Theorem 6 of Milgrom and Roberts (1990) applies. Furthermore, because the equilibrium investments are unique under our regularity conditions, ei ≤ ec . Therefore, by Lemma 2, Bc is always more efficient than Bi without cooperative investments.  This result establishes an important benchmark, namely, that the nexus of contracts, modeled in the form of an incomplete bargaining network, can only be efficiency-enhancing in a world with positive externalities. In other words, only when investments benefit other players’ productions as well as their own, is it meaningful to use the firm as a nexus of contracts to impose control structure over renegotiation. Given this benchmark, the rest of this section refers to a world with cooperative investment, and shows that bargaining control rights can indeed improve efficiency. The proof of Proposition 1 highlights that the efficiency of bargaining control rights lies in the relationship-specificity term vjk − (vj + vk ) and its interaction with investments. Based on these observations, we highlight two particular notions of relationship-specificity, which separately correspond to the benefit and the cost of incomplete bargaining networks. Definition. ∂vj ∂v + k. ∂ei ∂ei

Under fixed asset ownership structure A, investment ei is a cooperative synergistic investment (CSI) if

∂vjk > ∂ei

The CSI defines a relationship-specific cooperative investment, a more stringent requirement than solely cooperative investments. It requires the investment to improve the synergy between other players. One such example is mentoring

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junior professionals to work better with clients. Other things being the same, if ei is a CSI, then giving i bargaining control rights increases the marginal benefit of ei , which can consequently induce higher ei in the equilibrium of the investment game. Definition. Under fixed asset ownership structure A, investment ei is a self synergistic investment (SSI) with respect to player j if

∂vij ∂v ∂v > i + j. ∂ei ∂ei ∂ei

One sufficient condition to satisfy the SSI is that it is a relationship-specific self investment (i.e.,

∂vj ∂v ∂v = 0 and ij > i ), ∂ei ∂ei ∂ei

such as firm-specific human capital investments made by employees. Note that it is possible that ei is only a SSI with respect to k but not j. For instance, ei is only specific to cooperation involving both i and k. 17 Other things being the same, if ej is an SSI with respect to k, then giving i bargaining control rights decreases the marginal benefit of ej , which can consequently induce lower ej in the equilibrium of the investment game. Although the first-order effects of bargaining control rights are clear, the net effect on the equilibrium investment levels is generally ambiguous due to second-order interactions between players’ investments. Taking advantage of the asymmetric structures of the benefit and cost in using bargaining control rights, we are able to draw results in some special cases. 4.2.2. Efficiency of bargaining control rights The following propositions in this subsection present two scenarios where using bargaining control rights can be more efficient than in the GHM model. Proposition 2. Given asset ownership A, if no player’s investment is an SSI, and all investments are CSIs, then it is always optimal for some player to have bargaining control rights over others. Proof.

See the Appendix. 

More interestingly, even when investments are SSIs, as long as they are only relationship-specific with respect to one common player, it is efficient for this player to have bargaining control rights over others. Condition 1.

Players j and k’s investments are only SSIs with respect to player i.

Condition 2.

Only player i’s investment is a CSI.

Proposition 3. over others. Proof.

Given asset ownership A, under Conditions 1 and 2, it is always optimal for i to have bargaining control rights

See the Appendix. 

This result echos and generalizes the insights of Alchian and Demsetz (1972), wherein the firm arises as a nexus of contracts in order to relieve the inefficiencies in team production where externalities prevail. The difference is that Alchian and Demsetz (1972) focus on monitoring to correct for externalities, while we emphasize the adoption of bargaining control rights implied by the contractual networks. In fact, as a slight modification of their classical example, an investment in a monitoring technology by the owner operator of the firm can be viewed as a cooperative synergistic investment that improves synergy among workers in a team. In this case, the model implies that it is efficient to put the owner operator at the nexus of contracts to motivate such critical CSIs. 4.3. Allocation of both bargaining control rights and asset ownership The second key result is that once bargaining control rights become a design parameter in the governance structure, optimal asset ownership may be different from that seen in the GHM model. The intuition is that bargaining network and asset ownership do not affect ex ante investment incentives independently. Once the incomplete bargaining network alleviates the adverse effects of synergistic cooperative investments, asset ownership no longer needs to attend to this role and thus may be optimally allocated to other players. We first restrict asset ownership to sole investor ownership in Sections 4.3.1–4.3.2, an assumption we relax in Section 4.3.3. To keep the problem tractable, we focus on one-asset or two-asset cases. It is well known in the literature that the general optimal asset ownership prediction of the GHM model depends on specific assumptions regarding technology. However, one particularly robust result is that the optimal governance structure allocates asset ownership to the party with the most productive investments. This result remains generally true in our framework as well. Nonetheless, in this section, we highlight particular scenarios such that our model predicts an optimal governance structure where the investor making cooperative synergistic investments becomes the nexus of contracts, whereas the asset is controlled by other players regardless of how productive their investments are in the final value.

17

Moreover, an SSI may fail even when Assumption 1 holds. For instance, it may be that

∂v123 ∂ei

>

∂vi ∂ei

+

production, possibly to production involving both i and k, but not to the relationship with j excluding k.

∂ vj

∂ei

≥

∂vij ∂ei

≥

∂vi ∂ei

. In this case, ei is specific to joint

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4.3.1. Sole-player ownership with one asset By our regularity conditions, investments are weak complements with asset ownership. For expositional simplicity, we use the following definition and conditions to distinguish several cases of complementarity between investments and assets. Definition.

Investment ei is complementary (noncomplementary) to asset m with respect to S if ∂ vS is increasing (non∂ei

increasing) in asset m, that is, the ownership of m by S does (not) increase ∂ vS . Specifically, this requires ∂ vS (e, A) > (= ) ∂ vS (e, A ) for A(S) \ A (S) = m. 18

∂ei

∂ei

∂ei

Condition 3. (Player j is essential for the complementarity between m and any investment) ei , ej and ek are noncomplementary to m with respect to any coalition S−j without j. If j is essential for the complementarity between m and ei , then the contribution of ei is independent of m whenever j does not participate in production. We provide two such examples. If investment ei is a cooperative human capital investment on j, such as training or knowledge sharing, that is specific to the asset m, then j is essential for the complementarity between m and ei . Another example is that ei improves the asset m, but only j can utilize the improvement, such as an upgrade to a new big data system that requires j’s human capital to operate. Sometimes, the complementarity between m and ei is also relationship-specific (synergistic). For instance, m is a relationship-specific asset that is most productive when both j, k participate, and ei is coaching, training, or providing information for j and k to better utilize m, or ei is an investment in m. The following condition identifies an extreme case. Condition 4. (The complementarity between m and ei is purely synergistic with respect to j, k) ei is noncomplementary to m with respect to j or k individually, but is complementary when j and k produce together. In contrast, the complementarity between asset and investment may not be relationship-specific. In particular, investment ej may be learning and self-training in utilizing asset m, which can be valuable even without cooperating with other players. Condition 5.

(Investment ej is complementary to asset m without cooperation) ej is complementary to m with respect to j.

First, consider the case with only one productive asset. Without loss of generality, we focus on two different asset ownership allocations Ai and Aj , where asset m is owned by players i and j.19 Proposition 4. Under Conditions 1, 2, and, moreover, if Conditions 3–5 hold for asset m, then it is optimal for i to have bargaining control rights and Aj to be the optimal asset ownership, that is, (Aj , Bi ) is always optimal. Proof.

See the Appendix. 

This result contrasts sharply with the prediction of the GHM model (with cooperative investment), which yields Ai , i.e. (Ai , Bc ), as the optimal asset ownership, under the same conditions when ∂ vijk is sufficiently large.20 ∂ei

The intuition of this proposition hinges on our earlier result that the nexus of contracts protects incentives for CSIs. Under Conditions 3–5, asset ownership only affects ei through vjk . In the GHM model with cooperative investment, allocating the asset to j lowers ei , which is prohibitively costly if ei is highly productive in the final value vijk . Thus, the efficient arrangement may be Ai , allocating the asset to i as a “hostage,” separating the essential player j from the asset, and sacrificing ej in exchange for higher ei . Once we introduce the nexus of contracts, however, under Conditions 1 and 2, it is always efficient to make i the nexus of contracts, which subsequently mitigates her concern that j, k may cooperate without her. In this case, asset m no longer needs to perform the “hostage” role and thus can be more efficiently allocated to j. In short, under the specified conditions and the consequently efficient incomplete bargaining network Bi , allocating the asset to j improves ej without lowering ei , thus raising the efficiency of the transaction.

4.3.2. Sole-player ownership with two assets In this subsection, we turn to the two-asset case with M = {m1 , m2 } to discuss predictions related to integration versus non-integration, and to illustrate differences between the GHM model and our model with nexus of contracts. We use (i) Aii to refer to the asset ownership where i owns both assets, (ii) Aij to refer to the case where i owns m1 and j owns m2 , and (iii) Ajj to refer to the case where j owns both assets, etc.21

18 19 20 21

The notation “\” is the set difference operation, that is, M1 \ M2 = m if m ∈ / M2 and M1 = M2 ∪ {m}. k-ownership is equivalent to a relabeling of the players. See the online appendix for the proof of this statement. Formally, Aii is such that Aii ({i}) = {m1 , m2 }; Aij is such that Aij ({i}) = {m1 }, Aij ({j}) = {m2 }, and so on.

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This result follows from the previous proposition. Proposition 5. Under Conditions 1, 2, and, moreover, if Conditions 3–5 hold for both assets m1 and m2 , then it is always optimal for i to have bargaining control rights and Ajj should be the optimal asset ownership, that is, non-integration (Ajj , Bi ) is always optimal. Proof.

The proof follows directly from Proposition 4. 

Under the same conditions, the GHM model (with cooperative investment) predicts both asset integration Aii and firm integration, i.e. (Aii , Bc ), as the optimal asset ownership when ∂ vijk is sufficiently large. ∂ei

It is worth noting the differences of interpretation between the GHM model and our model. In the classical GHM model, when both assets are jointly owned by one player, the transaction is “integrated,” whereas when assets are separately owned by different players, the transaction is “non-integrated.” Thus, (Aii , Bc ) describes a case of asset integration. Because asset ownership is the only governance instrument, the transaction is thus interpreted as fully integrated. In our model with the nexus of contracts, however, integration refers to a case where the nexus of contracts also owns all assets. A player can “own a firm” either by controlling the nexus of contracts (as interpreted by AD), or by controlling assets (as interpreted by GHM). Thus, (Ajj , Bi ) is interpreted as an “assetless” firm controlled by i, employing k and contracting with another firm controlled by j, who owns all essential productive assets. One example of such “assetless” firm is professional service firms (PSFs) in areas such as law, design, consulting, or accounting. The conditions required in the proposition resemble a scenario where i’s investment is highly synergistic, cooperative, and asset-specific, whereas j’s investment is asset-specific and less relationship-specific. PSFs are well known for extensive mentoring, training, and information sharing from the senior partners, which increases cooperation between junior employees and their client firms. The investments of a PSF’s senior partners fit the requirements of i very well. Under these conditions, Proposition 5 made a prediction highly consistent with the prevalent phenomenon that experienced professionals own PSFs with few productive assets. It also offers a rationale for the fact that despite their highly valuable roles in economic transactions, PSFs neither integrate with nor are integrated by their client firms controlling most of the productive assets. The following proposition illustrates a case when the GHM model predicts asset integration but our model predicts asset non-integration. Proposition 6. Under Conditions 1, 2; if Conditions 3–5 hold for asset m2 ; and if ej and ek are noncomplementary to asset m1 with respect to any S = / {i, j, k}, then it is always optimal for i to have bargaining control rights and for Aij to be the optimal asset ownership, that is, non-integration (Aij , Bi ) is always optimal. Proof.

See the Appendix. 

Under the same conditions, the GHM model (with cooperative investment) predicts both asset integration Aii and firm integration, i.e. (Aii , Bc ), as the optimal asset ownership when ∂ vijk is sufficiently large. ∂ei

4.3.3. Joint asset ownership In this subsection, we return to the one-asset case with M = {m}, but allow for joint asset ownership. Joint ownership refers to the case where no player has residual rights of control over the asset, but all players have access to the asset as a / {i, j, k}. grand coalition. Specifically, joint ownership AJ is defined by AJ ({i, j, k}) = m and AJ (S) =∅ for any S = This subsection shows that in some cases, the GHM model predicts joint asset ownership, whereas our model predicts that nexus of contracts with sole ownership is more efficient than joint asset ownership. Condition 6.

(All investments are purely cooperative) ∂ vS = 0 for any S  i and S = / {i, j, k}, for all i = 1, 2, 3. ∂ei

Proposition 7. Under Conditions 2 and 6; if ei is noncomplementary to asset m with respect to {j}; and if ek is noncomplementary to asset m with respect to {i, j}, then it is always optimal for i to have bargaining control rights and for Aj to be the optimal asset ownership, that is, sole-player ownership with bargaining control rights (Aj , Bi ) is optimal comparing to joint ownership. Proof.

See the Appendix. 

Under these identical conditions, the GHM model (with cooperative investment) predicts joint ownership as optimal asset ownership, that is, (AJ , Bc ) is optimal.22 Since Che and Hausch (1999), the literature on the property rights theory of the firm found that joint ownership can mitigate the adverse effects of cooperative investments and improve investment incentives. Although shared asset ownership is common among homogeneous investors, such as senior professionals in partnerships, it is rarely shared among heterogeneous investors that the GHM model typically describes, such as one senior consultant, an engineer, or a machine shop manager.

22 The GHM prediction is well known in the literature. It is first shown by Che and Hausch (1999). Interested readers may refer to Proposition 12 in Segal and Whinston (2012) for details.

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Our model shows that in some special cases, the nexus of contracts can serve a similar role in protecting investment incentives when cooperative investment is prevalent in the transaction, thus freeing up asset ownership from joint ownership. 5. Discussion—incomplete bargaining networks In this article, an incomplete, but always connected, bargaining network implies that two of the three players are unable to implement decisions without approval from the third player. This arrangement gives the third player control beyond the ownership of assets. Many observations fit the characteristics of the boss’s control rights in ex post renegotiation. When it comes to bargaining over decisions, the owner operator of the firm bargains for the firm as a whole.23 Representing her subordinates, she bargains against other business firms and customers. Further, she bargains against her own subordinates, representing outside contractual relationships with other firms and customers. The subordinates have very limited rights to bargain with anyone other than their employer. One underlying institutional reason of these facts is that firms are legal persons in business contracts, whereas employees or divisions are not (Iacobucci and Triantis, 2007; Hansmann and Kraakman, 2000). With very few exceptions, most employees do not participate directly in bargaining with other employees and other outsiders. When they do, they typically bargain on behalf of their employer’s firm, not on behalf of themselves. Admittedly, firms may not have full control over subordinates’ bargaining power to completely block agreements between outsiders and subordinates. Yet, given the reasons we have discussed, it is likely that real-world firms have significant control over their subordinates’ bargaining rights. Because all proofs in this model rely on monotone comparative statics results, all the insights from this model can be readily generalized to environments with imperfect bargaining control rights. We sketch a simple extension here, where an exogenous parameter describes the intensity of bargaining control rights, which may be determined by the local institutions. Let intensity q be a value between 0 and 1. Then, the bargaining payoff for each player can be modeled by a linear combination of the payoffs under a complete network and the corresponding incomplete network, such as (1 − q)Yic + qY ii . In such a model, all our proofs will go through, and the qualitative implications would be identical to the insights of the current model. 6. Concluding remarks This article embeds the concept of the firm as a nexus of contracts in the framework of the property rights theory of the firm. We model the nexus of contracts as an incomplete bargaining network among players, and evaluate whether introducing restrictions in bargaining rights can improve efficiency in addition to property rights over assets. Our main finding is that when there is cooperative investment, using bargaining control rights can improve efficiency in addition to using asset ownership. Furthermore, the predicted optimal asset allocation can differ from the result prescribed in the classical GHM model. By modeling the nexus of contracts through the ex post bargaining network, the model subsumes the classical GHM governance structures as special cases with complete bargaining networks. Therefore, the model is able to address the effects of incomplete bargaining networks using the original GHM model as a benchmark, yielding rigorous results regarding implications on efficiency and possibly different asset ownership predictions. One can interpret this modeling framework to match many observed governance structures in the real world. Bargaining control rights resemble the vertical hierarchical structure in a business firm, which complements asset ownership in governing transactions among multiple players. This interpretation offers a theory of the firm without necessarily relying on asset ownership. This feature allows us to expand the scope of the property rights theory of the firm to understand assetless firms, such as PSFs, and employment relationships. Appendix. Proof of Lemma 1. For Yi to be non-decreasing in e−i , it is sufficient to show that the marginal contributions MSi by player i are non-decreasing in e−i . Notice

MSi =

⎧ vi ⎪ ⎪ ⎪ ⎪ ⎨ vS − vS\{i}

(1)if i isnotconnectedin S (2)if i isconnectedin S, and S\{i} isconnected

⎪ vS − vS\{i}1 − vS\{i}2 (3)if i isconnectedin S, but S\{i} isnotconnected ⎪ ⎪ ⎪ ⎩

23 Holmström (1999) notes that, “One possible explanation is that ownership strengthens the firm’s bargaining power vis-a-vis outsiders. Suppliers and other outsiders will have to deal with the firm as a unit rather than as individual members. . .The general point though is that institutional affiliation, and not just asset allocation, can significantly influence the nature of bargaining.”

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Regularity conditions of productive investment imply Case (1), and Assumption 1 implies Cases (2) and (3). Therefore, Yi is non-decreasing in e−i for all i.  Proof of Lemma 2. We show the result by contradiction. Let e* be the Nash equilibrium investment level of an investment game under some fixed governance structure g. Let eFB be the first-best level investment. Then, we define e = max{e∗ , eFB } as the pointwise maximum of e* and eFB . FB . By Assumption 2, Y has increasing differences in (e , e ); therefore, Suppose ei∗ > eiFB for some i, then ei > eiFB and e−i ≥ e−i i i −i ∗ ∗ Yi (ei , e−i ) − Yi (eiFB , e−i ) ≥ Yi (ei , e−i ) − Yi (eiFB , e−i ) > 0, ∗ , and (ii) by our where the second inequality strictly holds because (i) by the definition of e* , ei∗ is the best response to e−i regularity conditions on the production functions, the best response ei∗ is unique. Therefore, we have FB Yi (e) = Yi (ei , e−i ) > Yi (eiFB , e−i ) ≥ Yi (eiFB , e−i ) = Yi (eFB ),

where the second inequality holds by Lemma  1.  Yi (e) > Yi (eFB ), a contradiction to the definition of first–best investment This then implies the total social surplus is FB level e .  Proof of Proposition 2. By observing (4) when all players’ investments are CSIs, ∂ (vjk − vj − vk ) ≥ 0; thus, Yio has increasing ∂ei

differences in (ei , ). Moreover, ∂ (vjk − vj − vk ) = 0 when no player’s investment is a SSI (and under Assumption 1). Thus, ∂ej

by (5), Yjo has (trivial) increasing differences in (ej , ). By Assumption 2, Theorem 6 of Milgrom and Roberts (1990) applies. Furthermore, because the equilibrium investments are unique under our regularity conditions, ei ≥ ec . Therefore, by Lemma 2, Bc is always less efficient than Bi under the specified conditions.  By observing (4), because only ei is a CSI, ∂ (vjk − vj − vk ) ≥ 0, Yio has increasing differences in (ei , ∂ei ∂ ). Moreover, (vjk − vj − vk ) = 0 when ej , ek are only SSIs with respect to i (and under Assumption 1). Thus, by (5), Yjo has ∂ej

Proof of Proposition 3.

(trivial) increasing differences in (ej , ). By Assumption 2, Theorem 6 of Milgrom and Roberts (1990) applies. Furthermore, because the equilibrium investments are unique under our regularity conditions, ei ≥ ec . Therefore, by Lemma 2, Bc is always less efficient than Bi under the specified conditions. 

Proof of Proposition 4. Following Proposition 3, Bi is efficient regardless of asset ownership; thus, we have eBi ≥ eBc . Under Bi , the players’ payoffs are Yii

=

1 1 1 1 (v − vj − vk ) + (vij − vj ) + (vik − vk ) + vi , 3 ijk 6 6 3

Yji

=

1 1 1 (v − vik ) + (vij − vi ) + vj , 3 ijk 6 2

Yki

=

1 1 1 (v − vij ) + (vik − vi ) + vk . 3 ijk 6 2

We define notation



Y˜ ii (e, Ai , )

=

Yii (e, Ai )

if  = 0

Yii (e, Aj )

if  = 1,

and we define Y˜ ji and Y˜ ki similarly.

According to Conditions 3 and 4, ∂ vik , ∂ vi , and ∂ vj do not change with ownership of m. Thus, Y˜ ii has (weak) increasing ∂ei

∂ei

∂ei

differences in ei and . Also, following Condition 3, ∂ vi and ∂ vik does not change with ownership of m. Thus, Y˜ ki has (weak) increasing ∂ek

∂ek

differences in ek and . Following Condition 5, ∂ vj is increasing in m. Thus, Y˜ ji has increasing differences in ej and . ∂ej

By Assumption 2, Theorem 6 of Milgrom and Roberts (1990) applies. Furthermore, because the equilibrium investments are unique under our regularity conditions, eBi ,Aj ≥ eBi ,Ai ≥ eBc ,Ai . Therefore, by Lemma 2, (Bi , Aj ) is always more efficient than (Bc , Ai ) under the specified conditions. 

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Proof of Proposition 6. The result for m2 follows directly from Proposition 4. Because neither ej nor ek are complementary to m1 , allocating assets to player i only (weakly) increases every player’s marginal payoff. Thus, allocating m1 to i is optimal regardless of asset ownership and bargaining network. Combined with the result of Proposition 4, (Aij , Bi ) is the optimal governance structure.  Proof of Proposition 7. Since all investments are purely cooperative, no investment is an SSI. Thus, by Proposition 2, Bc is never efficient. Moreover, because only ei is a CSI, Bi is always more efficient. Given Bi , because ∂ vij is non-increasing in asset m, compared to AJ , allocating the asset to j does not lower the marginal ∂ek

payoff of k. Because ei is noncomplementary to m with respect to j, compared to AJ , allocating the asset to j does not the lower marginal payoff of i. Therefore, by the monotone comparative statics theorem, Aj is more efficient than AJ . Thus, (Aj , Bi ) is more efficient than (AJ , Bc ).  Appendix A. Supplementary Data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.jebo.2016.08.003. References Alchian, A.A., Demsetz, H., 1972. Production, information costs, and economic organization. Am. Econ. Rev. 62 (5), 777–795. Che, Y.-K., Hausch, D.B., 1999. Cooperative investments and the value of contracting. Am. Econ. Rev. 89 (1), 125–147. Chiu, Y.S., 1998. Noncooperative bargaining, hostages, and optimal asset ownership. Am. Econ. Rev. 88 (4), 882–901. de Fontenay, C.C., Gans, J.S., 2005. Vertical integration in the presence of upstream competition. RAND J. Econ. 36 (3), 544–572. de Meza, D., Lockwood, B., 1998. Does asset ownership always motivate managers? outside options and the property rights theory of the firm. Quart. J. Econ. 113 (2), 361–386. Grossman, S.J., Hart, O.D., 1986. The costs and benefits of ownership: a theory of vertical and lateral integration. J. Polit. Econ. 94 (August (4)), 691–719. Hansmann, H., Kraakman, R., 2000. The essential role of organizational law. Yale Law J. 110 (387). Hart, O.D., 1995. Firms, Contracts, and Financial Structure. Clarendon Press, Oxford. Hart, O.D., Moore, J., 1990. Property rights and the nature of the firm. J. Polit. Econ. 98 (6), 1119–1158. Holmström, B., 1999 April. The firm as a subeconomy. J. Law Econ. Organ. 15 (1), 74–102. Holmström, B., Milgrom, P., 1991. Multitask principal-agent analyses: incentive contracts, asset ownership, and job design. J. Law Econ. Organ. 7, 24–52. Iacobucci, E.M., Triantis, G.G., 2007. Economic and legal boundaries of firms. Va. Law Rev. 93 (515). Kranton, R.E., Minehart, D.F., 2000 Autumn. Networks versus vertical integration. RAND J. Econ. 31 (3), 570–601. Magnet, M., 1994. The new golden rule of business. Fortune, 60–64. Milgrom, P., Roberts, J., 1990. Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica 58 (6), 1255–1277. Myerson, R.B., 1977. Graphs and cooperation in games. Math. Oper. Res. 2 (3), 225–229. Nishiguchi, T., 1994. Strategic Industrial Sourcing: The Japanese Advantage. Oxford University Press, New York. Rajan, R.G., Zingales, L., 1998. Power in a theory of the firm. Quart. J. Econ. 113 (2), 387–432. Segal, I., Whinston, M.D., 2012. Property rights. In: Gibbons, R., Roberts, J. (Eds.), The Handbook of Organizational Economics, Introductory Chapters. Princeton University Press, Chapter 3. Segal, I.R., Whinston, M.D., 2000. Exclusive contracts and protection of investments. RAND J. Econ. 31 (4), 603–633. Whinston, M.D., 2003. On the transaction cost determinants of vertical integration. J. Law Econ. Organ. 19 (1), 1.