A Theory of Joint Ownership

Transcription

1 A Theory of Joint Ownership Maija Halonen 1 University of Bristol March This is a completely revised Chapter 2 of my LSE PhD thesis and a working paper Reputation and Allocation of Ownership. I am indebted to Oliver Hart and my supervisor John Moore for helpful discussions and encouragement. I would also like to thank Ian Jewitt and In-Uck Park for comments, and Godfrey Keller, Steven Matthews, Kevin Roberts, Seppo Salo, John Vickers, Iestyn Williams, and especially Patrick Bolton for comments on an earlier draft. This version beneþted from seminar participants at Bristol, Essex, Exeter, and Harvard. Financial support from the Academy of Finland, Foundation of Helsinki School of Economics, and Yrjö Jahnsson Foundation is gratefully acknowledged.

2 Abstract We show that joint ownership (partnership or joint venture) can implement Þrst best in a twice repeated game when each agent believes that the other party is honest with a very small probability. In the Þnal period the ownership structure is renegotiated because joint ownership is ex post inefficient. If an agent has cheated her outside option is very low since by cheating she has lost her reputation while an unrevealed agent has a much higher outside option. Therefore in renegotiation most of the surplus is distributed away from the cheater. Renegotiation provides a punishment mechanism so that Þrst best can be supported. JEL Classification numbers: D23, L14, L22 Keywords: Theory of the Þrm, reputation, joint ventures, partnerships

3 1 Introduction Partnerships have long been a puzzle for the economists. According to the present theory there is a more efficient way to organize production: no sharing rule can implement efficient actions in a partnership while efficiency can be attained by hiring a third party to break the budget (Holmström (1982)). Further, in the property rights theory of the Þrm (Grossman and Hart (1986) and Hart and Moore (1990)) joint ownership is a dominated structure. We show that when the agents care about their reputation partnership can be not only efficient but better than any other organizational form. 1 The property rights theory is based on agents opportunistic behaviour self-interest seeking with guile in Williamson s (1985) terminology. When there are quasi rents from the relationship due to Þrm-speciÞc investments and high transaction costs prevent writing a complete contract holdup problem typically arises. 2 An agent pays full cost of the investment but part of the value is expropriated in ex post bargaining. According to this theory ownership rights should be allocated to minimize the holdup problem. However, the behaviour we observe in the real world is not always opportunistic. Macaulay Þnds in his survey on contractual relations in business that: Businessmen often prefer to rely on a man s word in a brief letter, a handshake, or common honesty and decency even when the transaction involves exposure to serious risks. [Macaulay (1963), p. 58] This kind of behaviour can be explained by reputation concerns. When the one-shot gain from opportunistic behaviour is outweighed by the loss of trust in the future we should indeed observe loyalty and honesty. When reputation matters can we avoid holdup problems under any ownership structure? Is there any scope for allocation of ownership in a dynamic world? These are the issues raised in this paper. We show that joint ownership can implement Þrst best in a twice repeated game with incomplete information while the holdup problem cannot be avoided in a conventional hierarchical Þrm. 1 In Radner (1986) partnership can be efficient in a repeated game but it is not explained why partnership would be better than any other organizational form. 2 Grossman and Hart (1986), Hart and Moore (1990) and Bolton and Whinston (1993) build on Williamson (1975, 1985), Klein, Crawford and Alchian (1978) and Grout (1984) in analysing the holdup problem. 1

4 In our model each agent believes that the other party is honest with probability θ (which is very small) and otherwise opportunist. An honest agent keeps her word if the other party has kept his in the past while an opportunist keeps her word if it pays. Therefore any agent who breaches an implicit contract reveals herself as an opportunist. The agents can support Þrst best by the following arrangement. They write an explicit contract on joint ownership and agree implicitly to make Þrstbestinvestments. In the Þnal period ownership structure is renegotiated because joint ownership is ex post inefficient. If no deviation has occurred the renegotiation leads to a 50:50 split of the surplus. If an agent has cheated her outside option is very low because all the market has learned that she is untrustworthy. While the outside option of an unrevealed agent is much higher. Therefore in renegotiation most of the surplus is distributed away from the cheater and renegotiation provides a punishment mechanism. In a conventional Þrm with a single owner, which in our setup is the optimal structure in the one-shot game, cooperation cannot be sustained because the ownership structure is ex post efficient even after deviation. Since there is no renegotiation, there is no way to punish the cheater. This iswhyanarrangementthatseemsinefficient from a static point of view can be optimal in a dynamic context. An interesting feature of our model is that renegotiation occurs also in equilibrium. In related papers Klein and Leffler (1981), Telser (1981) and Bull (1987) show how cooperative agreements can be self-enforcing in a variety of situations. Their analysis relies on implicit contracts while in our model the interaction of implicit and explicit contracts is crucial. In Baker et al. (1995) and Ramey and Watson (1996), like in our model, outside market conditions are important to the level of investment that can be sustained in a relationship. They, however, assume that after deviation the agents split immediately. With important relationship-speciþc investments it may not be ex post efficient to split before the end of the project even if the implicit contract has broken down. This is the case we analyse. In Garvey (1995) reputation effects lead to a more equal sharing rule and the sharing rule is interpreted as the ownership structure. In our paper a range of sharing rules, equal and unequal ones, can implement ÞrstbestwhilethedeÞnition of ownership is who has the residual control rights over the assets. Further, in his model it is not clear what is the difference between nonintegration and joint venture since both could result in equal sharing. Finally, Watson (1996) analyses the dynamics of partnerships with incomplete information about the agents 2

5 patience. In our model organizational form is endogenous. The rest of the paper is organized as follows. The static model is presented in Section 2. Section 3 introduces our dynamic model. A repeated game with a single owner is analysed in Section 4 while Section 5 examines joint ownership. Section 6 derives the optimal ownership structure. Section 7 discusses the robustness of the results and Section 8 concludes by relating our results to the partnerships and joint ventures observed in the real world. 2 Benchmark: Static model Our benchmark is a simple version of Hart and Moore (1990). We analyse a setup where agents 1 and 2 use asset a to supply consumers. Ex ante each agent makes an investment in human capital which is speciþc to asset a. We model the investment as agent i directly choosing the value of the investment, v i. The investment makes the agent more productive in using the asset. The agent for example learns to know better the properties of the asset or the environment the Þrm operates and can therefore generate more surplus. The investment can be either cost reducing or value enhancing. The cost of the investment to agent i is c(v i ).Wemakethefollowingassumptions: Assumption 1. v i [0,V] where V > 0. c(v i ) 0 and c(0) = 0. c i is twice differentiable. c 0 (v i ) > 0 and c (v i ) > 0 for v i (0,V), with lim vi 0 c 0 (v i )=0and lim vi V c 0 (v i )=. Investment in human capital is assumed to be too complex to be described adequately in a contract. It is observable to both agents but not veriþable to third parties like the court. Therefore the agents choose the investments noncooperatively. We also rule out proþt-sharing agreements. 3 Ex ante contracts can only be written on the allocation of ownership. The possible ownership structures are agent 1 ownership, agent 2 ownership and joint ownership. Outside options play a key role in the analysis. Under agent i ownership i can work alone with the asset after the investments are sunk and sell the Þnal good to the customers. The value of the trade without agent j s contribution is λv i where 0 λ 1. Thevalueofλ depends on the importance of agent j as a trading partner. If agent j is indispensable to asset a so that giving 3 See Hart and Moore (1990) for the justiþcation of these assumptions. 3

6 the control of a to agent i does not enhance the surplus he can generate on his own, then λ =0. If agent j is dispensable so that agent i could replace her by an outsider without loss of value, then λ =1. We assume that the agents are equally important as trading partners (have identical λ 0 s). When an agent does not control the asset on her own she has an outside option to work for another Þrm. Weassumethatasseta is essential to the agents so that the outside wage does not depend on their investment. Without loss of generality we normalize this Þxed wage to zero. Ex post the uncertainty is resolved and the agents negotiate a spot contract. The investments are observable to both agents at the time of bargaining and therefore an efficient bargaining solution will be reached. The only source of inefficiency in this model arises from the possible underinvestment. We assume that the agents divide the gains from negotiation according to Nash bargaining. Finally, production occurs and the Þnalgoodissoldtothe customers. The timing of the game is illustrated in Figure Figure1here---- Equation (1) gives the Þrst best investments, v i : 1 c 0 (vi )=0 i =1, 2 (1) Since the agents are identical their efficient investments are equal and to simplify notation we drop the subscript; vi v. The Þrst best joint surplus is denoted by S. Since ex ante contracts on trade cannot be written, the bargaining takes place after the investments are sunk. Agent i foresees that part of the surplus she generates by her investment is expropriated in ex post bargaining while she pays the full cost of investment. Therefore underinvestment (holdup) typically arises. Ownership is allocated to minimize the holdup problem. Under joint ownership agent i can realize the value of her investment only by reaching an agreement with agent j ; her investment has no value if she does not have access to the essential asset. The agents have to reach a unanimous agreement to use the asset. Since both agents have zero outside options they split the surplus 50:50 and the payoffs for the agents are: P i = 1 2 (v 1 + v 2 ) c(v i ) i =1, 2 (2) 4

7 Therefore agent i receives only half of the value of her investment at the margin and the investments, v J 1 and v J 2, are given by: 1 2 c0 (vi J )=0 i =1, 2 (3) Again we simplify notation by writing vi J v J. Each agent s equilibrium payoff is denoted by P J and the joint surplus by S J. With a single owner, say agent 1 4, the payoffs for the agents are: P 1 = λv [(1 λ)v 1 + v 2 ] c(v 1 ) (4) P 2 = 1 2 [(1 λ)v 1 + v 2 ] c(v 2 ) (5) The investments, v 1 1 and v 1 2, are given by the following Þrst-order conditions: 1 2 (1 + λ) c0 (v1 1 )=0 (6) 1 2 c0 (v2 1 )=0 (7) Theowner sinvestmentisthegreaterthemoredispensabletheworkeris (the higher is λ) while the worker s investment does not depend on λ. Denote agent 1 s and 2 s equilibrium payoffs byp1 1 and P2 1 respectively, and the joint surplus by S 1. At date 0 the agents contract on a joint surplus maximizing ownership structure. It is easy to see from (3), (6) and (7) that joint ownership is strictly dominated for any λ>0. Under joint ownership no agent has an outside option, while when there is a single owner, the owner has a positive outside option and therefore improved incentives to invest. Hart and Moore (1990) obtain the same result in a more general setup. 3 The model In our dynamic model the stage game described in the previous section is repeated twice. We also introduce incomplete information in the model. Each 4 Since the agents are identical agent 2 ownership would give the same joint surplus as agent 1 ownership. 5

8 agent believes that the opponent is honest with probability θ and opportunist with probability (1 θ). An honest agent gets a large enough private beneþt from keeping her word so that she has a dominant strategy not to renege. We do not model this explicitly but simply take her strategy as given: an honest agent keeps her word if the other party has kept his in the past. Opportunist is the normal type (who does not get private beneþts) and keeps her word if it pays. We assume that θ is very small. At date 0 the agents write an explicit contract on the ownership structure and make an implicit contract on the investments and sharing rule. Ownership contract can be renegotiated at any time. Skills depreciate and the environment changes and further investments can be made at the beginning of period 2. We make the extreme assumption that the investment depreciates fully before the next period begins. In the second half of the period the spot contract on the division of surplus is written and the gains from trade are realized. Two types of outside options are relevant in the dynamic model. First, after the investments are sunk the agents can split and trade in the outside market. This was described in Section 2. Second, at the beginning of the period (before making the investments) the agents can split. If an agent has cheated we assume that the outside market will get to know this and the agent s payoff in the outside market is equal to zero. On the other hand, if the agent has kept her word her type is private information and she can earn ep h > 0 in the outside market if she is honest and e P o if she is opportunist. We assume that e P o > e P h but this assumption is not critical. What is important is that the outside option of an unrevealed opportunist is greater than that of a revealed opportunist. In other words, loss of reputation will result in a lower payoff in the outside market. Note that there is no contradiction between this reputation effect and nonveriþability of investments. Hard information is needed to win a court case but soft information is enough to cause an agent to lose her reputation. We assume that the outside options are low enough so that the agents would not split in the static game under optimal ownership structure. This is guaranteed by Assumption 2. Assumption 2. e Po <Min{P 1 1,P 1 2 }. The timing of the game is illustrated in Figure Figure2here---- 6

9 4 Repeated game with a single owner When the agents are in a long term relationship and care about the future, the holdup problems may not be so severe. In this section we analyse if the efficient investments can be supported in a twice repeated game with a single owner. If the agents are very patient and the probability of honesty is very high, Þrst best can be supported under any ownership structure. We are interested in situations when the agents are not completely patient and the probability of honesty is very small. At date 0 the agents implicitly agree to make the efficient investment and to share the surplus according to (P1,P2 ). (The sharing rule will be determined later.) Deviation from either the investments or sharing rule will reveal the agent as opportunist and the rest of the game will be played as the static game. In particular, if an agent cheats in investment the cooperation breaks down already in the second half of the day 5 : the surplus will be divided by Nash bargaining, not according to the efficient sharing rule. Also if there is no deviation in investment but an agent does not agree to follow the sharing rule (P1,P2 ), then bargaining will result in splitting the gains from trade. It is easy to see that cheating in investment dominates cheating in sharing rule. When an agent deviates in investment, she chooses her investment taking into account that the gains from negotiation will be divided evenly. (The deviation investment is thus equal to the investment in the one-shot game.) By deþnition this gives the agent a higher payoff than Þrst making the efficient investment and then switching to Nash bargaining. The interesting case to analyse is that of two opportunists. At date 0 the agents make an implicit contract on the investments and sharing rule. Our aim is to Þnd a sharing rule (P1,P2 ) such that efficient investments can be implementedinperiod1. Firstbestcannotbesupportedinperiod2since there is no point for an opportunist to build reputation in the Þnal period of the game. First best (pooling equilibrium) can be supported at date 1 5 Note that by cooperation we refer to efficient behaviour: Þrst best investment and sharing rule. Of course this is a noncooperative game. Note also that even during punishment the agents get together and make the deal but the investment is lower and the division of surplus is different. 7

10 if and only if the discounted payoffs from cooperating are greater than the discounted payoffs in the deviation path. Pi + δ θp c,1 i +(1 θ) Pi 1 P c,1 i + δpi 1 for i =1, 2 (8) where Pi is agent i s payoff under cooperation, P c,1 i is i s cheating payoff, and Pi 1 is i s payoff in the static game. Equation (8) gives the incentive compatibility constraints for the agents. By cooperating agent i will get Pi at date 1. At date 2 with probability θ agent j is honest and i collects the cheating payoff P c,1 i. With probability (1 θ) also agent j is opportunist and since they both cheat payoffsarethesameasintheone-shotgame,pi 1. While deviation at date 1 would give the cheating payoff P c,1 i, and the punishment payoff Pi 1 at date 2. Adding up the incentive compatibility constraints (8) and taking into account that (P1 + P2 )=S we have: S c,1 S δθ S c,1 S 1 (9) where S c,1 P c,1 1 + P c,1 2. The agents can Þnd a sharing rule (P 1,P2 ) such that neither agent has an incentive to cheat if and only if equation (9) holds. It is not necessary to know the exact division (P1,P2 ). Since at date 0 there is symmetric information an efficient bargaining outcome will be reached. Evaluating the aggregate incentive compatibility constraint (9) for θ = 0 gives: (10) does not hold since: S c,1 S 0 (10) S c,1 S = = 1 2 v (1 + λ) v1 1 c v (1 λ) v v1 2 c v2 1 [v1 c (v 1 )] [v 2 c (v 2 ½ 1 )] 2 (1 + λ) v1 1 c ¾ 1 v1 1 2 (1 + λ) v 1 c (v1) ½ v1 2 c ¾ 1 v2 1 2 v 2 c (v 2 ) > 0 (11) This expression is strictly positive since v1 1 is chosen to maximize the term in the Þrst square brackets and v2 1 is chosen to maximize the term in the third 8

11 square brackets. Intuitively it is clear that (10) does not hold; if the Þrst best surplus were greater than the sum of cheating payoffs we would not need to worry about cheating in the Þrst place. For (9) to hold θ has to be high enough. The Þnalperiodrewardfrom cooperation at date 1 arises from the opportunity to cheat an honest agent. When θ is very small, which we have assumed, there is no Þnal period reward and backward induction implies that cooperation cannot be supported at date 1. Theorem 1 summarizes this analysis. Theorem 1 In the unique perfect Bayesian equilibrium of a twice repeated game with a single owner the investments are equal to (v 1 1,v 1 2) in both periods. 5 Repeated game under joint ownership Joint ownership is a dominated structure in the static game and therefore in analysing the repeated game we have to take into account that the ownership structure will be renegotiated after deviation. Ownership structure may be renegotiated even if no deviation has occurred. In renegotiation the agents will trade the asset so that it has a single owner. We examine renegotiation in Subsection 5.1 before analysing the incentives to cooperate in detail in Subsection Renegotiation of ownership structure We will Þrst analyse renegotiation after deviation. Suppose agent i deviates at date 1 and thus reveals that she is an opportunist. After that it becomes optimal for the agents to renegotiate the ownership structure so that the asset has a single owner. We assume that each agent can make a take-itor-leave-it offer on the asset trade with probability 1. This extensive form 2 is chosen for tractability. If the agents fail to reach an agreement and split, the payoff for agent i, who has revealed herself to be an opportunist, is zero. Agent j s payoff is P e o if he is an opportunist and P e h if he is honest, and his type is his private information. These are the outside options. If the agents do not trade the asset but stay together, their payoffs arep J each, that is payoffs in the static game under joint ownership. This is their inside option. The surplus the agents are bargaining over is S 1 and the bargaining outcome depends on the relative sizes of outside and inside options. In what follows we analyse three cases. 9

12 If P J < P e h < P e o agent j would walk away if the agents fail to reach an agreement on the sale of the asset because his payoff in the outside market is greater than the payoff from staying in the Þrm which is jointly owned and where the implicit contract has broken down. Then the deviant s expected payoff at date 2 will be equal to: ½ 1 h bp i = Max 2 θ S 1 P e i h, 1 h S 1 P 2 e i ¾ o. (12) If agent j is in the position to make an offer he would offer zero to agent i. If i rejected the offer, j would walk away and i could only get a zero payoff in the outside market. If agent i can make the offer, she will either offer P e o whichbothtypeswouldacceptleaving ³S 1 P o e to agent i. Or she will offer P e h which only an honest agent would accept and therefore trade occurs with probability θ. If P e h < P e o P J the agents would not split even if they fail to trade the asset. Therefore agent i would not accept an offer lower than P J and similarly agent j would reject any offer below P J. Then agent i s expected payoff in period 2 is: bp i = 1 S 1 P J P J = 1 2 S1 (13) The third possibility is that P e h P J < P e o. Agent i s expected punishment payoff is then: ½ 1 bp i = Max 2 θ S 1 P J, 1 h S 1 P 2 e i ¾ o θp J (14) When agent i canmakeanoffer she either offers P e o whichbothtypeswould accept or P J which only an honest agent would accept. This explains the Þrst term in (14). The second term in (14) gives the payoff in the event that it is agent j s take-it-or-leave-it offer. By rejecting an offer agent i would get an expected payoff of θp J sinceanhonestagentwouldstayintheþrm even if the ownership structure is not changed. Therefore when agent j is in the position to make an offer, he offers θp J irrespective of his type. 6 6 Note that a separating equilibrium where e.g. an opportunist offers zero and an honest agent offers more than zero does not exist. If agent i believes that an agent who offers zero is opportunist, she will accept a zero offer. Knowing this an honest agent would offer zero as well. 10

13 We summarize the outcome of the bargaining after cheating in Lemma 1 for the case where θ = 0. Lemma 1 If agent i deviates under joint ownership at date 1 her payoff at date 2 is: ( 1 hs bp i = 1 e i ) ½ ¾ P 2 o if and only if P e > o P J. 1 2 S1 Lemma 1 says that when the inside option is greater than the outside option (and the agents would never split) the agents share the surplus 50:50. While when the outside option is greater than the inside option there is a credible threat of splitting and the cheater gets less than half of the surplus. The ownership structure can be renegotiated even if neither agent has cheated previously. Lemma 2 gives the result from this renegotiation. Lemma 2 If under joint ownership neither agent cheats at date 1, ownership structure is renegotiated at the beginning of date 2 and each agent gets a payoff 1 2 S1 at date 2. Proof. In the Appendix. It is clear that if ownership structure is renegotiated each agent gets half of the surplus. Since neither agent has cheated they have symmetric outside and inside options. Regardless of which options are relevant, bargaining results in an even split of the surplus. But will the agents renegotiate? Since the probability of honesty is very small, the joint surplus would be equal to Max ns J, 2P e o o if there is no renegotiation while by trading the asset so that it has a single owner generates a joint surplus equal to S 1.SinceS 1 > Max ns J, 2P e o o (by Assumption 2) the agents will renegotiate even if nobody has cheated. 5.2 Incentives to cooperate In this subsection we show that Þrst best can be supported in period 1 under joint ownership. At date 0 the agents implicitly agree to make Þrst best investments and share the surplus according to (P1,P2 ). In the efficient path the agents cooperate in the Þrst period and at the beginning of period 11

14 2 renegotiate the ownership structure (Lemma 2) and in effect the implicit contract. This change of ownership structure is not written in the explicit contract even it could be done because this way a punishment mechanism is provided. The incentive compatibility constraints for the agents are: P i + δ 1 2 S1 P c,j i + δ b P i for i =1, 2 (15) By cooperating agent i gets Pi in period 1. In period 2 the ownership structure is renegotiated and i gets the renegotiation payoff 1 2 S1. By cheating agent i receives date 1 payoff P c,j i after which ownership structure is renegotiated and i gets a payoff P b i. Adding up equations (15) we get the aggregate incentive compatibility constraint: ³ S c,j S δ S 1 S b (16) where S b ³ bp1 + P 2 b and S c,j that for P e o P J (16) is equivalent to: and for e P o >P J (16) is equivalent to: ³ P c,j 1 + P c,j 2. From Lemma 1 we know S c,j S 0 (17) S c,j S δ e P o. (18) Obviously when the inside options are greater than the outside options in renegotiation after cheating cooperation cannot be supported at date 1 because the date 2 payoffs are equal in the punishment path and in the efficient path (equation (17)) 7. While when the outside options are greater than the inside options Þrst best can be supported if and only if (18) holds. This proves our main result. Theorem 2 Joint ownership implements Þrst best in period 1 in a perfect Bayesian equilibrium if and only if e P o >P J and δ S c,j S / e P o. 7 S c,j S =2 1 2 v vj c v J 2[v c (v )] =2 1 2 vj c v J v c (v ) > 0 12

15 First best can be supported at date 1 because renegotiation provides a punishment mechanism. Ownership structure is renegotiated at date 2 whether cheating has occurred at date 1 or not. But while renegotiation in the efficient path leads to a 50:50 split of the surplus, in renegotiation after cheating the surplus is distributed away from the cheater. If the aggregate loss from cheating (δp e o ) outweighs the aggregate one-shot gain S c,j S the agents can Þnd a sharing rule (P1,P2 ) such that pooling equilibrium occurs at date 1. An interesting feature of our model is that renegotiation occurs also in equilibrium. The agents know that the ownership structure will be renegotiated at date 2 in and off the equilibrium but they deliberately leave the date 0 contract silent about it to ensure a punishment mechanism. In a sense this gives an endogenously incomplete contract. When there is a single owner Þrst best cannot be supported because ownership structure is ex post efficient even after deviation. Since there is no renegotiation there is no way to punish the deviant. 8 This is why an arrangement that seems inefficient from a static point of view can be optimal in a dynamic context. In our model the interaction of implicit and explicit contracts is important and Þrst best can be supported even if the probability of honesty is very small and the game is repeated only twice. In Kreps et al. (1981) and Fudenberg and Maskin (1986), which rely on implicit contracts alone, the horizon has to be very long for cooperation to occur for a very small probability of honesty. Our result depends crucially on the outside option P e o. First, Po e has to be greater than P J so that the threat of splitting is credible in renegotiation and the punishment mechanism starts to work. Second, the higher is P e o, the smaller is the deviant s share of the surplus, the higher is the loss from cheating, and therefore the better are the incentives to cooperate. Outside option measures dynamic speciþcity of human capital. In our model human capital is fully speciþc within a period. That is, if an agent learns skills they have no value outside the Þrm. But at the beginning of the next period the agent has to learn new skills whether she stays in the Þrm or not. If it is very difficult for her to learn the skills required in a new Þrm in the outside 8 Even the ownership structure is ex post efficient the agents could still renegotiate something under single ownership. E.g. if agent 1 deviates agent 2 could at the beginning of date 2 threat to quit if he does not get a transfer from agent 1. However, Assumption 2 guarantees that this threat is not credible; inside options are always greater than outside options when there is a single owner. 13

16 market, outside option is low, and the agent s skills are Þrm-speciÞc in a dynamic sense. If she can learn new skills in any Þrm equally well, outside option is high and her skills are not speciþc in a dynamic sense. Accordingly, joint ownership implements Þrst best when there is friction in the short run but human capital is not dynamically Þrm-speciÞc. Suppose the incentive compatibility constraint (18) is not satisþed. Can the incentives to cooperate be improved by lowering the target level of investment? That is, the agents implicitly agree to make an investment slightly lower than Þrst best. Suppose the agents agree to choose target investments v. Denote the joint surplus these investments generate by S and the aggregate cheating payoffs withthesetargetinvestmentsbys c,j. Substituting these in the aggregate incentive compatibility constraint (18) we have: 1 δp e o + S S c,j = δp e o +2[v c (v)] 2 2 v vj c v J 0 (19) Changing the target investment a little has the following effect: ³δP e c,j o + S S 1 =2 v 2 c0 (v) (20) At v = v (20) is negative because c 0 (v )=1. Therefore a smaller target level makes cooperation easier (aggregate incentive compatibility constraint (19) becomes less binding). Decreasing investment has only a second order effect on S but a Þrst order negative effect on S c,j. By cheating an agent can expropriate half of a lower investment and therefore the gain from cheating decreases. We further know that for any investment above v J c 0 ( ) > 1 2. Thus reducing the target investment makes cooperation easier until the target investment is equal to v J. Naturally the agents are only interested in implementing a higher investment than v J, the worst outcome of the static game. 6 Optimal ownership structure After having examined the two possible ownership structures we now turn into analysing the optimal structure. At date 0 the agents contract on a joint 14

17 surplus maximizing ownership structure. Choosing either single or joint ownership results in date 2 surplus equal to S 1. Therefore the optimal ownership structure is the one that maximizes date 1 surplus. Date 1 surplus is equal to S 1 when there is a single owner. There are two cases when it is optimal to have a single ³ owner. J First, if the inside options are greater than the outside options epo P there is no punishment mechanism under joint ownership and the resulting surplus at date 1 is equal to S J.SinceS 1 >S J the agents choose single ownership. ³ J Second, if the outside options are greater than the inside options epo >P so that the punishment mechanism starts to work under joint ownership but the agents are so impatient that no surplus greater than S 1 can be supported, then it is optimal to have a single owner. That is: ³ δ< S c,j S / P e o for all v v 1,v (21) where v 1 denotes the symmetric investments that result in joint surplus equal to S 1. In all the other cases joint ownership generates a higher surplus. This proves Theorem 3. Theorem 3 Joint ownership is optimal if and only if Po e ³ >P J and δ S c,j S / P e o for v = v 1. Theorem 3 says that when joint ownership implements at least S 1 at date 1 then it is optimal. At date 0 the agents negotiate the ownership structure, the target levels of investments and the sharing rule. Only the Þrst (ownership structure) can be written in the explicit contract but promises can be given about the investments and sharing rule. Since bargaining is under symmetric information an efficient outcome will be reached. If and only if the conditions in Theorem 3 are satisþed the agents choose joint ownership. In addition to that they agree to make investments that generate the highest joint surplus. Accordingly, if ³ δ S c,j S / P e o (22) does not hold for v = v they cannot implement Þrstbestbutwillagreeon the highest investments for which (22) holds. 15

18 7 Robustness The previous analysis shows that joint ownership can be optimal in a dynamic context. We chose a relatively simple setup (one asset and two identical agents) to clearly bring out the driving forces. Would we expect the same result in a more general framework? If there are many assets and many asymmetric agents there is more than one inefficient ownership structure in the static game. Since all the ex post inefficient ownership structures are renegotiated at date 2 there is a potential punishment mechanism in all those structures. Then the question arises whether joint ownership provides the best punishment mechanism. The advantage of joint ownership is that notonlyisitexpostinefficient but it minimizes the agents inside options and therefore makes it most likely that the punishment mechanism starts to work. In a T-period model Þrst best can be supported for some ( but less than T- 1) periods even with a single owner if T is large enough. But joint ownership can still be optimal since it can implement ÞrstbestforallbuttheÞnal period of the game. The aim of the date 0 explicit contract is to design an ownership structure that gives the best incentives to cooperate, that is, gives the maximum punishment relative to gain from deviation. Joint ownership provides the punishment mechanism but on the other hand the gain from deviation is highest too. Under joint ownership the outside options (after the investments are sunk) are zero and by cheating the agents can extract half of the value of the opponent s Þrst best investment and therefore gain a lot from deviation. While a single owner has a positive outside option and therefore a deviating worker cannot extract as much as half of the value of the efficient investment in bargaining. As a result the gain from cheating is smaller when there is a single owner. This is why in our two-period model a time-dependent explicit contract (1,J) dominates (J,J). ((1,J) denotes a contract that assigns single ownership for date 1 and joint ownership for date 2.) The contract (1,J) restricts the date 1 gain from deviation to be minimal and provides the maximum date 2 punishment. However, in a T-period model this would mean that a contract (1,J,J,...,J,J) gives better incentives for date 1 than a contract (J,J,J,...,J,J). Period 1 differs from all the other periods of the game by being the Þrst period of the game; since there is no past punishment mechanism is not needed. In any other period it is crucial to have a punishment mechanism and therefore to have joint ownership. Thus it is true that 16

19 (1,J,J,...,J,J) provides better incentives for date 1 than (J,J,J,...,J,J) but the date 1 incentive compatibility constraint is never critical in the Þrst place. The incentive to cheat is increasing in time because the less periods there are left the less likely it is that the one-shot gain from deviation is outweighed by the punishment. To implement ÞrstbestforallbuttheÞnal period it is the date (T-1) incentive compatibility constraint that is critical. Therefore contract (J,J,J,...,J,J) is actually equally good in implementing Þrst best than contract (1,J,J,...,J,J). An ownership structure we have not analysed in this paper is outside control, that is giving ownership of the asset to a third party. 9 The residual rights of control are deþned by the owner having the right to decide all usages of the asset in any way not inconsistent with a prior contract (Hart (1995)). Therefore if the bargaining breaks down the agent does not have access to anassetanoutsidepartyownsortoanassettheuseofwhichrequiresa unanimous decision with another agent. Thus the outside options (after the investments) are zero at the margin 10 under both outside control and joint ownership and these structures are equivalent in the static model. However, in the dynamic context this equivalence disappears. Under joint ownership if the renegotiation of ownership structure after cheating fails and the noncheating agent walks away the cheater cannot use the asset and has to go to the outside market too even his payoff there is zero. While with outside control one (non-owning) agent leaving the Þrm does not stop the other agent staying in the Þrm. Therefore even if the outside option is greater than inside option for the non-cheating agent, the inside option is always relevant for the deviant. The deviant would not accept a zero offer since he can get more than that by staying in the Þrm. Thus joint ownership and outside control are not equivalent and in particular joint ownership dominates outside control since it punishes the deviant more. In a static framework where there is more than one asset, e.g. agent 1 operates asset a 1 and agent 2 operates asset a 2, joint ownership is equivalent to cross ownership (agent 1 owns a 2 and agent 2 owns a 1 ) and nonintegration with strictly complementary assets 11. In all these structures outside options after the investments are zero at the margin. Again the equivalence 9 Rajan and Zingales (1996) analyse outside control within the framework of the property rights theory. 10 That is, the value of the outside option does not depend on investment. 11 In de Meza and Lockwood (1996) nonintegration can be optimal for strictly complementary assets. 17

20 disappears in a dynamic model because the outside options before the investments differ. If bargaining on asset trade fails, the deviant leaves to the outside market with an asset under both cross ownership and nonintegration while with joint ownership he cannot take any assets with him. With more than two agents joint ownership can be interpreted as a partnership with a unanimity clause. However, often partnerships involve majority rule rather than unanimity. Partnership with majority rule can provide equally good punishment than unanimity when outside options are greater than inside options. If bargaining fails all but the deviant would go to the outside market. Since the acceptance of a majority is needed to use the asset, the deviant has no choice but to leave without any assets. We made a simplifying assumption that the types are revealed only after the date 0 contract is written. Therefore we did not have to analyse date 0 bargaining in detail since it is enough to know that an efficient outcome is reached in bargaining with symmetric information. Even if the types were revealed Þrst our results would not change. Assume agent 1 is honest. At date 0 bargaining she could make an offer that only one type accepts thus revealing the opponent s type. But since there is a very small probability that the other agent is honest agent 1 is better off not knowing it for sure. If she knows that agent 2 is opportunist Þrst best cannot be supported. Therefore she is happy with somebody pretending to be honest. Neither does agent 1 wish to reveal her type to agent 2. If agent 2 knew agent 1 is honest he would cooperate in period 1 and cheat in period 2. Although an honest agent does not like reneging it does not mean that she enjoys being cheated, which would happen if she revealed her type. Thus an honest agent would not reveal her type. 8 Partnerships and joint ventures We have shown that joint ownership can implement Þrst best. To conclude we will relate our results to the forms of joint ownership observed in the real world. Partnership is the main organizational form in professional services industries. Accounting Þrms, law practices, consulting and architectural Þrms, and medical clinics are often partnerships. In professional services human capital and in particular Þrm-speciÞc human capital is important. Knowledge about the Þrm s practices, colleagues, and customers is crucial for a high value service. And human capital is what drives our model. Our result 18

21 depends on the assumptions about the outside options. First, we assume that the outside market gets to know when an agent cheats. Professionals typically network across Þrms which allows them to exchange information and word will get around about an untrustworthy colleague. Second, it is assumed that the outside option for an unrevealed agent is relatively high in particular higher than what the agent could earn in a partnership where the implicit contract has broken down. In other words we assume that the agent s human capital is not dynamically Þrm-speciÞc (although within a period human capital is assumed to be fully speciþc). Although there is friction in the short run since it takes time for a professional to learn the practices of anewþrm she has a high level of general education (which is often stipulated by professional norms) and after a while she will learn the skills necessary in the new Þrm. Since the new Þrm is better organized either by implicit or explicit contract the professional can earn a high wage there. Accordingly, the assumptions behind our result seem to be satisþed in professional services industries. Joint ventures are another type of joint ownership. Joint ventures are often transitional arrangements. Our model captures this feature; joint venture is reorganized to a conventional hierarchical Þrm in the Þnal period. Joint ventures are often formed to develop a particular product and therefore the horizon is not very long. When the purpose of the venture is fulþlled it is dissolved. Maybe the reason why we do not observe professional partnerships being reorganized to conventional Þrms is that their horizon is much longer (or even close to inþnity) than the limited horizon of a joint venture. If at least one of our assumptions does not hold then the results of the static game apply. If human capital is not important (only effort is) as for relatively unskilled labour, if human capital is dynamically Þrm-speciÞc as for workers with relatively low level of general education, or if there is no good mechanism to exchange information unlike in a well-deþned, relatively small group of professionals, then we should observe a conventional hierarchical Þrm. This seems to match with the real world observations. 19

22 Appendix ProofofLemma2. When neither agent has cheated previously types are private information. If P J < P e h < P e o and it is agent i s opportunity to make a take-it-or-leave-it offer (with probability half) she will offer either P e o which both types will accept or P e h which only an honest agent accepts and therefore trade would occur with probability θ. Since θ is very small agent i will offer P e o. Likewise when agent j is in the position to make an offer he will offer P e o. Therefore agent i s renegotiation payoff is equal to: 1 hs 1 P 2 e i o + 1 P 2 e o = 1 2 S1 (A.1) If P e h < P e o P J each agent will offer P J while if P e h P J < P e o the optimal offer is P e o both leading to a 50:50 split of the surplus. Nowweknowtheexpectedpayoffs if ownership structure is renegotiated at the beginning of date 2 even if there has been no cheating. But will the agents renegotiate? Consider Þrst the case P e o P J. An opportunity of a take-it-or-leave-it offer arrives to agent 1 and she will initiate renegotiation if and only if: S 1 P J θp c,j +(1 θ) P J (A.2) where P c,j is agent 1 s cheating payoff under joint ownership. The left-handside of (A.2) gives her payoff from making the lowest acceptable offer to agent 2. The right-hand-side of (A.2) gives her payoff if she does not make any offer: with probability θ the opponent is honest and she gets the cheating payoff under joint ownership while with probability (1 θ) he is opportunist and agent 1 gets P J. For θ = 0 (A.2)isequivalenttoS 1 >S J. Obviously equation (A.2) holds and agent 1 will initiate renegotiation. If P J < P e o and agent 1 is in the position to make a take-it-or-leave-it offer, she makes an offer if and only if: S 1 P e o P e o (A.3) The left-hand-side of (A.3) gives agent 1 s payoff when she makes the lowest acceptable offer to agent 2 (knowing that with probability (1 θ) he 20

23 is an opportunist.) If agent 1 did not initiate renegotiation she would walk away since in the outside market she can earn e P o while staying in the jointly owned Þrm would give her a lower payoff θp c,j +(1 θ) P J. This explains why we have e P o in the right-hand-side of (A.3). We can rewrite (A.3) as 1 2 S1 > e P o (A.4) By Assumption 2 (A.4) holds since the smaller of the two agents payoffs cannot be larger than half the surplus. 1 2 S1 Min ª P1 1,P1 2 > Po e (A.5) Therefore it is optimal for agent 1 to initiate renegotiation. 21

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26 Date 0 Date 1 contract agents make spot contract on ownership investments on trade Figure 1 renegotiation of ownership? Date explicit contract agents learn invest- trade invest- trade on ownership, their type ments ments implicit contract on investments and sharing rule Figure 2