Professor Huihua NIE, PhD School of Economics, Renmin University of China HOLD-UP, PROPERTY RIGHTS AND REPUTATION

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1 Professor uihua NIE, PhD School of Economics, Renmin University of China OD-UP, PROPERTY RIGTS AND REPUTATION Abstract: By introducing asymmetric information of investors abilities and finitely reeated games into the classic hold-u model, this aer revisits the relationshi between roerty rights and reutation under incomlete contracting environment and obtains some different insights. First, even facing holdu agents can make efficient investments due to the reutation effect in some eriods of relationshi, which is sharly contrary to existing research. Second, although reutation is an incentive tool for agents, roerty rights are comlementary or even necessary for reutation, and reutation itself is not enough to motivate agents to make first-best investments without ownershi. Third, this aer exlains underinvestment, efficient investment, and overinvestment in a unified dynamic model of roerty rights. Keywords: hold-u; roerty rights; asymmetric information; reutation; incomlete contracts JE classifications: 4, 22, D23. Introduction In the real world, eole usually sign simle trading contracts. These simle contracts do not secify all of the rules for every conceivable eventuality, so they are incomlete contracts. In the resence of relationshi-secific investments, incomlete contracts will lead to hold-u roblems and ex ante inefficient investments, but vertical integration can alleviate hold-u because of ex ost adation within hierarchy (Williamson, 985). Based on this idea, a formal roerty rights theory of the firm has been rovided to show that aroriately allocating ownershi can motivate agents to make second-best investments (Grossman and art, 986; art and Moore, 990; hereafter GM), which significantly influenced the direction of research on the boundary of firms, cororate finance, government scoe, law and economics, and institutional design in the last twenty years. In contrast to the role of ownershi as a solution to reduce the investment inefficiency roosed by the roerty rights theory of the firm, there are three strands of literature arguing that efficient investment can be achieved by other solutions in an incomlete contracting environment. First, mechanism literature emhasizes the roles of message game (Aghion et al., 994), otion contracts (yon and Rasmusen, 2004), and contractual time design (Guriev and Kvasov, 2005). Second, reutation literature argues that market reutation can eliminate

2 uihua Nie hold-u and assure investment efficiency (Coase, 988). The third strand of literature discusses the interaction between ownershi and reutation (Baker, et al., 2002; alonen, 2002) in infinitely reeated games. While alonen (2002) considers joint ownershi to be otimal, all three literatures assert that efficient investment can be achieved irresective of ownershi. Interestingly, art (200) does not think that reutation will add new insight to static roerty-rights models, so it is worth revisiting the role of roerty rights, and the interaction of roerty rights and reutation in a dynamic environment. By introducing asymmetric information of investors ability in a finitely reeated game, this aer discusses the relationshi between roerty rights and reutation and rovides some different insights. First, I find that even facing holdu agents can make efficient investments due to the reutation effect in some eriods of relationshi, which is sharly contrary to existing research. Second, although reutation is an incentive tool for agents, roerty rights are comlementary or even necessary for reutation, and reutation itself is not enough to motivate agents to make first-best investments without ownershi. Third, this aer exlains underinvestment, efficient investment, and overinvestment in a unified dynamic model of roerty rights. Comared to existing literature on reutation and ownershi (e.g., Baker et al., 2002), the assumtion of finite game is weaker in this aer, and ownershi has a ositive effect for agents incentive in investment. In Baker et al. (2002) and alonen (2002), more asset ownershi increases the involved arties temtations to renege on the relationshi, so relational outsourcing or joint ownershi can be an efficient organizational structure. owever, in this aer, integration ( relational emloyment in terms of Baker et al.) is still the otimal ownershi model when there is one-side investment, which is consistent with the static model in GM. To elicit some results from the model in this aer, let us consider a slightly modified story of art and Moore (990). On an island, there are many skiers and tycoons, who stay for two days. A tyical skier can rovide cruise services for a tyical tycoon with a yacht. The cruise can bring the tycoon utility with a robability that deends on the skier s rivate tye. A skier can be an exerienced hand or an inexerienced hand, which is unknown to the tycoon. With the same sunk learning costs, an exerienced skier can rovide a successful service for a tycoon with a higher robability than an inexerienced skier can. Of course, the tycoon wants to search for an exerienced skier and refers to fire an inexerienced one if, the next day, he recognizes that the skier lacks exerience. The value of a successful service rovided by a articular skier to a tycoon is unverifiable by a third arty, so the skier faces holdu by the tycoon. Even so, to get a good reutation on the first day, under certain conditions, the skier would like to make secific investments according to the first-best standard to signal the behavior of an exerienced hand and then make second-best secific investments on the second (last) day. Facing loss on the first day, the more hysical assets there are, the more willing the skier is to make a first-best This aer also discusses the case without assets and two-asset case, while Baker et al. (2002) is silent on this.

3 old u, Proerty Rights and Reutation secific investment. Formally, in a two-eriod game model with asymmetric information, this aer argues that contractual incomleteness can lead to hold-u but that, due to the reutation effect, hold-u does not necessarily lead to inefficient investment. This aer contributes to the existing reutation literature by combining the reutation effect with roerty rights. On one hand, since the 980s, there have been a large number of studies on reutation mechanisms ioneered by Kres and Wilson (982) and Milgrom and Roberts (982) (hereafter KMRW). olmstrom (999) shows that market reutation rovides incentives for managers to make efforts, but first-best investment levels cannot be achieved. Unlike this aer, revious literature takes reutation as a vehicle to maintain trade that has nothing to do with hold-u and roerty rights. This aer takes reutation as an incentive tool comlementary to roerty rights in dynamic environments. This aer resonds to Tirole s criticism (999) that incomlete contract theory neglects the role of asymmetric information by combining the symmetric information of investment level and the asymmetric information of investors ability. For a long time, comlete contract theory and incomlete contract theory have diverged on the assumtion of informational symmetry. This is not the first aer that introduces asymmetric information in hold-u models. Other aers either assume that there is asymmetric information in investors costs or benefits (e.g., Bac, 993), or they use static hold-u models (e.g., Matouschek, 2004). Recently, Aghion et al. (202) revisited the truth-telling mechanism and discovered that hold-u still exists in incomlete contracting environments. Given that hold-u exists, this aer analyzes investment efficiency and is comlementary to Aghion et al. (202). The rest of this aer roceeds as follows: section 2 builds on a hold-u model with asymmetric information and describes a searating erfect Bayesian equilibrium and a ooling erfect Bayesian equilibrium in a case with one asset and a one side investment; section 3 further analyzes the incentive effect of all kinds of ownershi structures in a case with two assets and one side investment; and section 4 summarizes conclusions and lays out imlications for future research. 2. The Model 2. Setu Suose that there are Agents (e.g., skiers) and Agents 2 (e.g., tycoons), and there is one hysical asset a (e.g., a yacht). All agents are risk neutral and ossess boundless wealth. A air consisting of Agent and Agent 2 meets randomly and signs a contract, which secifies that Agent uses asset a and her secific human caital to suly a certain widget (W ) to Agent 2, who in turn uses W and his hysical assets (if ossible) to suly a final roduct to the market. There are two kinds of Agent : high-tye ( ) with high roductivity and low-tye ( ) with low roductivity. With the same cost, high-tye and low-tye Agent can enhance the value of W to with robability or ( 0 ), resectively, while they may fail and obtain zero value with

4 uihua Nie robability and, resectively. stands for Agent s investment level or value. Agent s tye is rivate information, and the robability for each tye of Agent is Agent 2 can observe only successful investment by Agent. Agent 2 does not invest, and his contribution to the final roduct is a fixed value (V ), so the joint surlus is V with a robability. Agent s investment costs are C( ), which are strictly convex. et 0, C(0) 0, C( ) 0, and C( ) 0. Because investment is too comlicated to be secified in an initial contract, the contract is incomlete. After the nature of the situation is clear, the costs and values of both arties investments are symmetrical, so ex ost bargaining can be efficient according to Coase theorem, though Agent s tye of information is asymmetric. 3 There is no side ayment, and two arties share the surlus according to a symmetric Nash bargaining solution. 4 When the relationshi breaks, if Agent owns hysical asset a and a secific investment succeeds, her outside otion is. If Agent has no asset or the secific investment fails, her outside otion is 0. [0,] indicates the economic relationshi between two agents. When another agent is indisensable, =0; otherwise, =. The game lasts for two eriods with a discount factor of (0,]. In eriod 2, according to Bayes rule, Agent 2 can udate his belief based on Agent s investment in eriod, which affects his decision to cooerate with Agent. If Agent 2 quits working for Agent, he can find emloyment with another Agent with robability in the market. ere 0, which reresents the search costs for agent 2. Meanwhile, we suose that after breaking u with Agent 2, the robability that Agent can find another agent 2 to cooerate with is ; otherwise, Agent can sell her hysical asset at a fixed rice of A. For simlicity, we normalize A as 0. 5 To summarize, the timing is as follows. In eriod : () Agent s tye and corresonding roortions are selected by nature. (2) Agent and Agent 2 meet randomly and sign a contract. (3) Agent makes an ex ante investment in human caital. (4) The state of nature is clear, and the two arties renegotiate. In eriod 2: (5) Agent 2 udates his belief in Agent s tye and decides whether to kee the relationshi or not, which determines whether Agent searches for another 2 It is just for convenience, but it will not qualitatively change our main conclusions. 3 It is noted that there is no contradiction between ex ost bargaining and asymmetric information about Agent s tye. 4 There is no sharing rule because the costs, benefits, and investment are observable to both arties but not verifiable to a third arty. 5 It is not a strong assumtion. Even we suose at that time agent s outside otion is, our main conclusion still holds.

5 old u, Proerty Rights and Reutation Agent 2. (6) Agent makes an ex ante investment in human caital if she cooerates with Agent 2 or sells her hysical assets at a fixed rice. (7) Renegotiation haens if Agent works with an agent 2. (8) Game over. 2.2 One eriod et us start with a simle case in which there are two agents, Agent and Agent 2, one hysical asset, a, and one eriod. As a benchmark, at first we consider the first-best standard to maximize total social surlus. Because high-tye Agent can generate more social surlus than low-tye Agent, to make things interesting, we suose that the market refers high-tye Agent. 6 The objective function of social welfare is Max ( ) 0 V C( ). () The first-order condition (FOC) is C( ) (2) Because of the convexity of the cost function, the solution to equation () exists and is unique. Equation (2) characterizes the standard of first-best secific investment in human caital, i.e.,, and it is efficient. Next, we discuss investment efficiency under different allocations of roerty rights and game structures. There are two subclasses: Agent owns a, or Agent 2 owns a. In incomlete contracting environments, Agent and Agent 2 indeendently choose the otimal strategy and obtain Nash equilibrium. Because Agent is the only one who makes an ex ante secific investment in human caital, we will focus on Agent s investment efficiency. If Agent owns a, her outside otion is or 0, but high-tye and low-tye Agent have different exected oututs. Secifically, Agent s objective functions of exected revenue and corresonding FOCs are the following. For high-tye Agent : V Max [ ( V )] ( ) C( ) (3) 2 2 ( ) C( ). (4) 2 For low-tye Agent : 6 I will justify the assumtion below.

6 uihua Nie V Max [ ( V )] ( ) C( ) (5) 2 2 ( ) C( ). (6) 2 Agent 2 does not make a secific investment, so his exected revenue deends on Agent s tye with an equal robability, i.e., ( ) ( ) [ V ( ) V ] [ V ( ) V ]. (7) Because, the exected revenue brought by a high-tye Agent (the first square bracket in the above exression) is more than that brought by a low-tye Agent (the second square bracket). Agent 2 is referred to a high-tye agent, which is the reason we take high-tye Agent s efficient investment level (exression (2)) as the first-best standard. If Agent 2 owns a, Agent s outside otion is 0. Similar to exression (3) or (5), we can get Agent s FOC, C( ) for high-tye (8) 2 C( ) for low-tye. (9) 2 FOC conditions (4), (6), and (8), (9) characterize Agent s otimal investment level with and without hysical assets, resectively. Notice that ( ) ( ) and. Comared to the first-best standard, two kinds of Agent underinvest, i.e., Agent s secific investment is second-best in a one-eriod game, because Agent can only get half the marginal revenue of a secific investment facing holdu by Agent 2, so Agent does not have sufficient incentive to invest ex ante. In addition, two kinds of agent with hysical assets invest more than in a situation without hysical assets. In fact, Agent s investment incentive is increasing with her outside otion which deends on the value of the hysical asset she owns and her imortance in the relationshi. Proosition : If only Agent invests and there is only one asset, both high-tye and low-tye agents make second-best secific investment in the one-eriod game. Agent s incentive to invest in secific human caital is increasing the value of the hysical asset. Proosition suggests that Agent will underinvest under hold-u and that

7 old u, Proerty Rights and Reutation the hysical asset will increase Agent s bargaining ower and her incentive to invest ex ante. These oints are in the sirit of the GM model. Due to adverse selection from asymmetric information of an agent s roductivity, allocating bargaining ower to an investing arty does not assure first-best secific investment in a one-eriod game because Agent always has the incentive to claim that she is high-tye, regardless of her real tye. Even in a finite-eriod game, first-best investment cannot always be achieved, which is what we will show in the next section. 2.3 Two Periods Suose that the games last for finite eriods 7, say T 2. For a finitely reeated game, the solution to a two-eriod game is similar to that of an N-eriod game. Without generality, we assume T 2, and we will discuss the case of T 2 in detail soon. Because a high-tye () agent will bring higher exected revenue than a low-tye () agent, Agent 2 would like to cooerate with a high-tye agent. Because the game is reeated and Agent s roductivity is asymmetric information, at the beginning of eriod 2, Agent 2 can udate his information based on Agent s investment level in eriod. Agent anticiates that situation, and in eriod, she has an incentive to signal her investment level to Agent 2. Naturally, the reutation effect works. The logic behind this model is similar to the signaling model; however, here an agent s signal (investment) itself is useful for roduction, and roerty rights have a role. In a reeated game, there are a lot of equilibria. What concerns us is whether Agent makes an efficient secific investment when facing holdu by Agent 2 in equilibrium. A. Searating PBE Because high-tye Agent has higher exected revenue in a secific investment with the same cost than low-tye Agent, a single-crossing condition is satisfied. By construction, naturally, there would be a searating equilibrium. Notice that when 0, the value of the hysical asset is 0. First, we concentrate on the case in which Agent owns hysical asset a, and then we comare it to the case without a hysical asset. We can construct a searating erfect Bayesian equilibrium (PBE) where both 7 Almost all of the dynamic hold-u models adot the infinitely reeated game aroach (e.g., Che and Sakovics, 2004). owever, as art (200) oints out, that reutation effect can lead to any ossible result, regardless of any organizational forms. Of course, it will be not interesting.

8 uihua Nie tyes of Agent choose different signals in eriod,, such that Agent 2 s osterior beliefs are Pr ob( s ), Pr ob( ) on the equilibrium ath, and s Pr ob( s ) 0 on the off-equilibrium ath ( s stands for searating ). Agent 2 fires any low-tye Agent and hires another Agent in the market with a robability of. Because eriod 2 is the last eriod, both tyes of Agent definitely make second-best secific investments ( j, ) in eriod 2. If Agent does not want to kee the relationshi with Agent 2, her otimal strategy is to invest j, which obviously dominates any other strategy. For high-tye Agent, if she makes her first-best secific investment in human caital in eriod, she will be regarded as high-tye and can kee cooerating with Agent 2 in eriod 2. 8 If she makes any other investment, with robability, she can find another Agent 2 to cooerate with, or with robability, she will fail to find another Agent 2 and receive zero (or a fixed ayment for her hysical asset). er incentive comatibility constraint is ( ) V ( ) V ( ) V ( )[ C ( )] 2 2 [ C( )] [ C( )] j. (0) For low-tye Agent, it is too costly for her to retend to be high-tye, so she would rather make a second-best investment in eriod. Once she discloses her real tye, she has to quit working for Agent 2 and search for another Agent 2 to cooerate with at robability in eriod 2. If she cannot find an Agent 2 to cooerate with, she will get zero with robability. As a result, her incentive comatibility constraint is: 8 In this case, Agent and Agent 2 build a kind of relational emloyment in terms of Baker et al. (2002).

9 old u, Proerty Rights and Reutation ( ) V ( )[ C ( )] 2 2 ( ) V ( ) V [ C( )] [ C( )]. () For Agent 2, on the one hand, he must have no incentive to deviate once he meets a high-tye Agent, even if high-tye Agent makes a second-best investment in the second eriod. On the other hand, he must have an incentive to search for another Agent in eriod 2 once he finds Agent is low-tye in eriod. In that case, he meets a high-tye or a low-tye Agent with equal robabilities. is incentive comatibility constraints are ( V ) ( ) V ( V ) ( ) V [ ] [ ] ( V ) ( ) V ( )[ ] 2 2 (2) ( V ) ( ) V ( V ) ( ) V [ ] ( ) { [ ] ( V ) ( ) V ( V ) ( ) V [ ]} ( )[ ] where,, and are determined by conditions (2), (4), and (6), resectively. It is noted that Agent 2 ends cooeration with Agent, who did not, given Agent s beliefs, make an equilibrium investment level in eriod. For high-tye Agent, if she deviates from the equilibrium investment level (say, and even makes investment (3) ), Agent 2 has an incentive to quit because he exects that Agent is low-tye. Actually, in this case, a high-tye Agent has no incentive to deviate, unless we emloy a more strict refinement aroach below. Now, we will discuss these incentive constraints. In condition (0), by making a first-best investment, high-tye Agent burdens some loss in eriod because is her otimal investment decision under static environments, but she will be comensated in eriod 2. Given the costs function, if the loss is sufficiently small (i.e., ) in eriod, or the reayment is sufficiently large (i.e., and is sufficiently small) in eriod 2, then condition (0) holds.

10 uihua Nie Condition () requires the mimicking cost to be sufficiently high (i.e., 0 or 0 ) or the reayment to be sufficiently low (i.e., 0 or ) to induce low-tye Agent to indicate her real tye. Notice that there is a tradeoff: the larger the benefit in eriod 2, the more motivated a high-tye Agent has to be to make a first-best investment, and the more motivated a low-tye Agent has to mimic a high-tye one. As for Agent 2, because his exected revenue is increasing in Agent s investment, condition (2) is loose for. Condition (3) holds if the search cost is sufficiently small (i.e., 0 ) or the difference in roductivity between the high-tye and low-tye Agent is sufficiently large (i.e., ). Considering the continuity of, in some certain arameters, i.e., is sufficiently small or,, or is aroriately moderate, constraints (0), (), and (3) can be satisfied simultaneously. Given Agent 2 s belief, the strategies of both high-tye and low-tye Agents are otimal. Meanwhile, Agent 2 s strategy is otimal, and his belief is consistent on the equilibrium ath, so we have a searating PBE. Proosition 2: If only Agent invests and there is only one asset, a searating PBE exists. In this equilibrium, high-tye Agent makes a first-best secific investment in eriod, and low-tye Agent makes a second-best secific investment in eriod. igh-tye Agent and low-tye Agent make second-best secific investments in eriod 2. The reasoning behind roosition 2 is very straightforward. Facing a loss resulting from deviating from a second-best investment in eriod, high-tye Agent will be subsidized in eriod 2 because of her good reutation. Conversely, low-tye agent has less exected roduction than high-tye in eriod 2, even if she can imitate the high-tye in eriod, which will not offset her loss in eriod. Although it could be a PBE at s, we can consider other cases. According to the intuitive criterion of refinement (Cho and Kres, 987), under certain arameters, a high-tye Agent can reduce her investment by an infinitesimally small amount below the efficient level, if the low-tye agent would never find it beneficial to make the same investment no matter the inference of Agent 2. So, there could be a case where s exists. In this case, the situation is a little better than the one-eriod game, where high-tye Agent makes more, but not efficient, secific investments. There could also be another case with s. In that case, high-tye agent overinvests, which is not efficient. It is very difficult to artition arameter saces for all of the cases exactly, but there

11 old u, Proerty Rights and Reutation is a tendency, other things being equal, that the further the distance s over, the more high-tye Agents exerience loss in eriod and the smaller the robability that a searating PBE exists. The oint is that there exists an equilibrium in which Agent will make a first-best investment under some conditions, which is what we want to emhasize in this article. When the mimicking benefit is large enough for low-tye Agent to make a secific investment, there can be a ooling PBE. B. Pooling PBE In a ooling PBE, both high-tye and low-tye Agents make the same secific investment in eriod : is such that Agent 2 s osterior beliefs are Pr ob( ) Pr ob( ) 0.5 on the equilibrium ath and Pr ob( ) 0 on the off-equilibrium ath ( stands for ooling ). Both kinds of agent 2 make a second-best secific investment of j ( j, ) in eriod 2. Agent 2 kees cooerating with Agent, who makes secific investment, and Agent 2 fires the Agent who makes other investments and then finds another Agent with a robability of in eriod 2. To construct a ooling PBE, high-tye Agent s incentive comatibility constraint is the following, which is the same as (0): ( ) V ( ) V ( ) V ( )[ C ( )] 2 2 [ C( )] [ C( )]. (4) ow-tye Agent s incentive comatibility constraint is ( ) V ( ) V ( ) V ( )[ C ( )] 2 2 [ C( )] [ C( )]. (5)

12 uihua Nie On the equilibrium ath, both high-tye Agent and low-tye Agent have no incentive to deviate. Because Agent makes a first-best investment that will bring more exected revenue for Agent 2 than making a second-best investment, Agent 2 s incentive comatibility constraint is automatically satisfied. Secifically, it is ( V ) ( ) V ( V ) ( ) V [ ] { [ ] ( V ) ( ) V ( V ) ( ) V [ ]} ( ){ [ ] ( V ) ( ) V [ ]} (6) When the future benefit is sufficiently large (i.e.,, or 0 ) or the difference in roductivity between high-tye and low-tye Agent is sufficiently small (i.e., ), constraints (4) and (5) can be satisfied simultaneously, and we have a ooling PBE. Proosition 3: If only Agent invests and there is only one asset, a ooling PBE exists. In equilibrium, both high-tye and low-tye Agent make a first-best secific investment in eriod, and they make second-best secific investment in eriod 2. Similarly, a ooling PBE can exist in other cases excet for. If exists, the secific investment is still inefficient, though it is better than the one-eriod game. In this case, according to intuitive criterion, the high-tye Agent must have an incentive to deviate until or even in the sace of a certain arameter, which is the searating PBE. If exists, this situation will not haen because high-tye Agent must have an incentive to deviate until at least. If exists, both kinds of Agent overinvest, which, again, is not efficient. In sum, there could be an equilibrium where both kinds of Agent invest efficiently, which is not

13 old u, Proerty Rights and Reutation achieved in the static holdu model. 3. The Otimal Ownershi Structure 3. No Physical Asset For Agent Now let us discuss the role of hysical assets for Agent to achieve first-best investment. Physical assets are imortant because they affect agents investment incentives via outside otions. Remember that Agent s exected revenue is increasing with her outside otion, which imlies that given the first-best standard of secific investment (i.e., condition (2)), an Agent with more hysical assets has looser incentive constraints than an Agent without hysical assets, regardless of being a high-tye or low-tye Agent. There is no doubt that hysical assets will highly affect Agent s incentive to make a first-best investment. To make the oint clearer, we take the searating PBE as an examle. Now we suose that Agent has no asset, but Agent 2 has the only asset and his outside otion is V. Without hysical assets, high-tye Agent s incentive comatibility constraint is ( ) V ( ) V ( ) V ( )[ C ( )] 2 2 [ C( )] [ C( )]. (7) Comared to the case with one hysical asset (condition (0)), given the same cost of first-best investment, high-tye Agent must bear more loss in eriod but gets less exected revenue. In articular, when the cost of searching for another Agent 2 is sufficiently small (i.e., ), condition (7) cannot hold. Because of, it is more imossible that low-tye Agent s incentive constraint holds under the same situation. So, we have roosition 4. Proosition 4: If Agent has no hysical asset and the search cost for Agent 2 is sufficiently small ( ), the first-best investment cannot be achieved. Proosition 4 indicates that roerty rights rovide a basis for the reutation effect. That is to say, when agents face hold-u under incomlete contracting environments, the reutation effect does not rovide sufficient incentive for agents to make first-best investments, while roerty rights can alleviate the tension between hold-u and investment efficiency. owever, reutation has nothing to do with roerty rights in a traditional reutation model (e.g., KMRW model). In sum, roerty rights have a first-order effect on an agent s investment level, and reutation has second-order effect on investment level. We will further discuss

14 uihua Nie the role of roerty rights below. 3.2 Two Physical Assets To build a theory of firm scoe, we suose that there are two hysical assets, a and a 2. These two hysical assets initially belong to and are essential to Agent and Agent 2, resectively. Only Agent invests. With his own hysical asset, the outside otion for Agent and Agent 2 is and V, resectively. With two hysical assets, the outside otions for Agent and Agent 2 are 2( A2) and ( V A), resectively. j ( j,2 ) indicates the imortance of Agent j as a trade artner. If Agent j is indisensable, then ; if not, then. A j indicates the value of asset j a j dearting from Agent j. et 0 j for j, 2, 0 A A, and 0 A2 V. Following the GM model, we define firm boundaries for the ownershi structure of hysical assets. We discuss five kinds of ownershi structures: (a) non-integration ( NI ), i.e., Agent and Agent 2 own asset a and a 2, resectively; (b) integration I ( I ), i.e., Agent owns both assets, and Agent 2 has no asset; (c) integration II ( I 2 ), i.e., Agent 2 owns both assets, and Agent has no asset; (d) joint ownershi ( JO ), i.e., both agents jointly own both assets, and neither agent can use any asset without consensus from the other; and (e) cross ownershi (CO ), i.e., Agent owns asset a 2, and Agent 2 owns asset a. In the forgoing discussion, we know that Agent s incentive to make a first-best investment is increasing with her outside otion, which is determined by the hysical assets she owns. The best ownershi structure is the one that rovides the most outside otions for Agent. It is evident that Agent has the most outside otions under integration I ( 2( A2) ), which is followed by non-integration ( ), and then followed by integration II or a joint or cross ownershi structure. Under the last three ownershi structures, Agent has no outside otion, which is similar to the case without hysical assets. Proosition 5: If only Agent invests and there are two assets, integration I is the otimal ownershi structure that can motivate Agent to make a first-best secific investment in eriod. We have shown that roerty rights still matter in dynamic environments. It turns out that integration I is still suerior to other ownershi structures, which is different from alonen (2002) but consistent with art (995). It also indicates that relational outsourcing (in terms of Baker et al. (2002)) cannot be the otimal ownershi structure when only one side invests. 3.2 Extensions Theoretically the conclusion of a two-eriod game can be naturally extended to a finite-eriod game with T 2. When T is small, it is only easy to rove that both tyes of Agent make first-best secific investment in ooling PBE if the marginal return to investment under ownershi structures is sufficiently large or the j

15 old u, Proerty Rights and Reutation robability of reetition is sufficiently large. The high-tye Agent makes first-best secific investments in searating PBE from eriod to eriod T, and both tyes of Agent make second-best secific investments in the last eriod T. owever, if T is very large, things may change. Making a first-best secific investment means a loss comared to making a second-best secific investment. On one hand, it tends to searate PBE, while on the other hand, it imoses too much loss for high-tye Agent, so that even a high-tye Agent has no incentive to make a first-best investment as a signal. 9 We have only considered one-side investments, but the main conclusions can be naturally extended to the situation in which both Agent and Agent 2 invest and have rivate information regarding tyes. Similar to the case with one-side investment, we can characterize a searating PBE or a ooling PBE in which both Agent and Agent 2 make a first-best investment. 4. Conclusion Introducing agents asymmetric information of investors ability in a dynamic hold-u model, this aer revisits the role of roerty rights in relation to the reutation effect and sheds lights on several theoretical oints. First, this aer shows that hold-u does not necessarily lead to inefficient investment due to the reutation effect under some conditions, roviding a stronger argument comared to existing models. Second, this aer demonstrates that roerty rights still matter even in dynamic environments and that roerty rights rovide a basis for the reutation effect. Third, integration has a ositive effect on agents incentives in relational contracts, which is contrary to the literature on ownershi and reutation (e.g., Baker, et al., 2002). In addition to introducing asymmetric information of agent tyes into a hold-u model, this aer rovides a ossible way to model ex ost inefficiency, which will be helful to exlain authority, hierarchy, and delegation from a new ersective. Drawing on these theoretical contributions, we still have some questions to solve. First, if we relax the assumtion that Agent and Agent 2 meet randomly, we can consider the matching roblem between different tyes of agents. In a broader environment, roerty rights, search costs, and reutation will interact, which raises more comlex questions and requires more sohisticated models. Second, we need more emirical tests or exeriments on hold-u to hel us understand investment efficiency in the real world. Acknowledgements I am greatly indebted to Professor Oliver art for many invaluable discussions and continuous encouragement when I visited arvard University as a ost-doc. I also thank Nicola Gennaioli, Enying Zheng, Jie Zheng, and articiants in the Organizational Economics Brownbag seminar at arvard University for helful comments. The financial suort from China National Excellent Doctoral Dissertation Grant (No ) is gratefully acknowledged. 9 We do not consider the case T because in this case, roerty rights do not matter when the discount factor is sufficiently large, and the conclusion converges to the case of finite eriod when the discount factor is sufficient small.

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