Motivating Information Acquisition through Organization Design

Transcription

1 Motivating Information Acquisition through Organization Design Heikki Rantakari University of Southern California Marshall School of Business This Version: July 7, 27 Abstract We investigate how monetary incentives and the allocation of decision rights inside an organizational hierarchy can be used together to motivate information acquisition, support accurate communication and guide decision-making. We analyze the di erences between a centralized decision-making structure, where local divisions acquire information and communicate it to the headquarters that makes the decisions, and a decentralized decision-making structure, where the local divisions not only acquire information but also retain decision-making authority. Under both governance structures, the basic tension of incentive provision is between providing strong local incentives to motivate information acquisition and balanced global incentives to motivate accurate communication and to guide decision-making. However, because the value of information and the value of incentive alignment depend on the allocation of decision rights, each governance structure arises as the preferred choice under speci c conditions. In particular, centralization is preferred only when coordination is su ciently important and motivating information acquisition is more valuable than incentive alignment. Contact: heikki.rantakari@marshall.usc.edu. Preliminary and Incomplete. This paper is based on Chapter 2 of my Ph.D. Dissertation. I would like to thank my advisors Robert Gibbons and Bengt Holmström for many helpful discussions and continuous encouragement. All remaining errors are naturally my own.

2 Introduction One common argument used to rationalize the existence of organizations is their ability to coordinate interdependent activities. However, organizations also exhibit signi cant heterogeneity in their internal organizational structure. This paper examines how the operating environment of an organization in uences the preferred choice of organizational architecture. Taking the organizational challenge to be one of coordinated decision-making under distributed information, such as constructing a coordinated sales and marketing strategy or coordinating product development e orts, we analyze how the allocation of decision-making authority and the monetary incentives provided to the organizational participants can be simultaneously used to motivate information acquisition, manage internal communication and to guide decision-making, and how the two are in turn determined by environmental conditions such as the degree of interdependence between the organization s activities, volatility of the environment and the cost of information. The organization consists of two (symmetric) divisions, the pro tability of which depends both on how well the activities of the divisions are aligned with local conditions and on how well the divisions coordinate their activities with each other. The organization is operated by three self-interested agents, with two of the agents running the local divisions and the third agent managing the headquarters. Information about the local conditions faced by each division is only available at the divisional level and has to be actively acquired by the division managers (local agents) at a personal cost. Information is thus local and distributed, and we also assume that the information acquired is soft, in the sense that the agents can talk about the information they (claim to) have acquired, but they cannot veri ably reveal any of this information. While information acquisition is localized, we assume that decision rights about how the divisions are operated can be reallocated inside the organization. We consider two alternative governance structures. Under centralization, control of both divisions is allocated to the headquarters (manager), while under decentralization, control of the divisions is retained by their respective local agents. After information acquisition, the local agents strategically communicate this information (through cheap talk) to the decision-maker(s), and the decision-maker(s) then choose decisions that 2

3 maximize their individual payo s (as determined by the endogenously chosen compensation structure) given the information available to them. Finally, while information cannot be acquired at the level of headquarters, the manager is able to improve divisional pro ts by devoting costly attention to them. Thus, all three participants need to be motivated through monetary incentives to perform their respective roles appropriately. The basic incentive provision problem under both governance structures is clear. While motivating the manager is relatively straightforward since balanced incentives lead to both good decision-making and good choice of e ort provision, the local agents face an inherent multitasking problem. On the one hand, local incentives are needed to induce information acquisition. On the other hand, balanced incentives are needed to induce accurate communication and, in the case of decentralization, appropriate decision-making. The question is then what factors determine the optimal balance between the two and how this balance is in uenced by the allocation of decision rights. The analysis of the model establishes three broad results. First, the equilibrium degree of inter-divisional con ict (as measured by the amount of pro t-sharing between the divisions) is generally decreasing in the importance of coordination under both governance structures. Second, the equilibrium degree of inter-divisional con ict is decreasing in the volatility of the environment and increasing in the cost of information. Third, centralization arises as the preferred allocation of decision rights only when coordination is su ciently important and information is costly relative to its value, so that the equilibrium inter-divisional con ict is su ciently high (conditional on the importance of coordination). The intuition behind this equilibrium outcome arises from two basic observations. First, the quality of primary information, communication and decision-making are substitutes in terms of overall organizational performance while complementing each other s marginal value. Thus, given the allocation of decision rights and the underlying parameters, the equilibrium strength of incentives depends simply on whether at a given level of inter-divisional con ict it is more e cient to motivate additional information acquisition (increase con ict) or to transmit and use the existing information better (decrease con ict). An increase in the importance of coordination both decreases the value of primary information and increases the value of accurate communication and decision-making, supporting increased pro t-sharing. Further, the higher the quality of primary information at a given level of inter-divisional con ict, 3

4 the more valuable accurate communication and decision-making become, supporting increased pro t-sharing. In other words, the higher the value of information, the higher the quality of information acquired by the local agents, given the existing compensation structure. This increase in the quality of primary information increases the value of incentive alignment and causes substitution from motivating information acquisition to motivating accurate communication and decision-making. Second, while the governance structures share the qualitative features of how the equilibrium compensation structure is determined, the allocation of decision rights matters because it in uences the equilibrium quality of decision-making and communication, and so both the perceived and true value of information, given the existing compensation structure and the underlying parameters. In particular, whenever coordination is su ciently unimportant, then the improvement in decision-making achieved through centralization is never su cient to compensate for the initial informational advantage held by decentralization and in consequence, decentralization is always preferred. In contrast, whenever coordination is su ciently important, either centralization or decentralization can be preferred, depending on the underlying parameters. This result follows because decreasing the inter-divisional con ict impacts the quality of communication and decision-making at di erent rates. In particular, while the quality of decision-making exhibits decreasing returns to incentive alignment, the quality of communication exhibits increasing returns to incentive alignment. In consequence, after a certain degree of incentive alignment between the local agents is achieved, the remaining returns come primarily in terms of improvements in communication under both governance structures. Because centralization is more dependent on accurate communication, decentralization is again preferred. It is only when primary information is relatively costly (so that the equilibrium compensation structure exhibits su cient inter-divisional con ict) that the improvement in decision-making achieved through centralization dominates the informational advantage of decentralization. Taken together, these results suggest three observations. First, the common association of centralization with weak incentives is not necessarily due to centralization requiring weak incentives as such, but instead that both are needed when the organization needs to maintain a su cient level of coordination among its activities. Second, in contrast to what is often argued, high divisional interdependence need not lead to centralized decision-making. Instead, either centralization or decentralization can be 4

5 preferred, depending on the cost and value of information centralization is preferred when motivating information acquisition is relatively more important and decentralization is preferred when the need for accurate information transmission dominates. Third, the model provides a partial rationalization for the common argument that decision rights should be located with directly informed agents. However, in the present setting this result doesn t arise from di culties of information transmission per se, but instead from the fact that incentive alignment improves decision-making faster than it improves communication, thus tilting the net balance in favor of decentralization. The remainder of the paper is structured as follows. Section 2 reviews the related literature and section 3 describes the model. Section 4 derives the equilibrium outcome under centralization and decentralization and section 5 analyzes the equilibrium. Section 6 concludes. Appendix A outlines the general solution that accounts for asymmetries across the divisions and Appendix B discusses how asymmetries between the divisions, in terms of importance of adaptation, coordination and environmental volatility, impact both the incentive provision and the allocation of decision rights. 2 Related Literature This paper contributes to and is related to the literatures on authority, strategic communication, coordination and incentive provision in organizations. The model builds directly on the framework of Rantakari (27a) and Alonso, Dessein and Matouschek (26), but instead of considering the outcome conditional on an exogenous degree of incentive alignment between the divisions and an exogenous quality of information, we endogenize both the degree of incentive alignment and the quality of information acquired by the divisions. In consequence, the paper is more closely related to Friebel and Raith (26), Dessein, Garicano and Gertner (26) and Athey and Roberts (2), each of which looks at the simultaneous determination of incentives and decision-making authority from alternative angles. The paper most closely related to ours is Friebel and Raith (26), who analyze a model where the divisions need to exert e ort to generate good-quality projects and the amount of resources available for implementing the project can be determined either before or after the e ort choice. The basic trade-o is thus between motivating e ort to improve the likelihood of good-quality projects 5

6 and motivating truthful revelation of that quality to improve resource allocation. While interim resource allocation contains an element of coordination, the underlying problems are qualitatively di erent. To illustrate, in their model, decentralization is always associated with zero incentive alignment because if interim reallocation of resources is desired, the headquarters is always in a better position to do so. In contrast, in our model, one of the key determinants of the choice of governance structure is the relative degree of equilibrium incentive alignment achieved under the two governance structures. Also, e ort to acquire information is qualitatively di erent from e ort to improve the likelihood of good-quality projects. As in Friebel and Raith (26), the basic trade-o in Dessein, Garicano and Gertner (26) is between local incentives to induce e ort provision and balanced incentives to induce truthful communication. The organization needs to decide when to implement synergies. A functional manager learns the returns to synergy implementation while two divisional managers learn the cost of implementing those synergies in terms of compromised adaptation. Again, incentive alignment is needed to induce truth-telling by the divisional managers and appropriate synergy implementation decisions, while local incentives are needed to induce productive e ort. However, because the productive e ort is orthogonal to the synergy implementation decision, the links among the value of information, the value of incentive alignment and the allocation of decision rights are not analyzed in DGG. Finally, Athey and Roberts (2) consider a problem where two agents need to be motivated to exert productive e ort. In addition, somebody needs to decide which projects (that impact the payo s to both agents) to implement. If one of the agents is allowed to make decisions, then he faces a multi-tasking problem analogous to the other papers: local incentives to induce e ort and global incentives to induce good project implementation decisions. Introducing a third agent as the decision-maker helps to solve this multi-tasking problem. As in DGG, e ort provision and project choice are orthogonal. Further, information about the projects can be made readily available to the manager, so that the use of a third agent is always bene cial unless it carries an additional cost. In contrast, in our model, the problem of strategic communication limits the use of an initially uninformed agent as the decision-maker. In addition to these papers, the present paper is more distantly related to number of other papers. Cheap talk: Communication, both between the local agents and to the headquar- 6

7 ters, is modeled as cheap talk. As a result, the model is related to the literature on cheap talk that has followed the seminal article of Crawford and Sobel (982). By considering multiple senders, the setting is closer to Battaglini (22), but since the agents obtain only partial and independent information, inducing truth-telling is impossible absent monetary transfers. Also, the possibility of preference alignment between the sender and the receiver makes the payo structure more related to Stein (989) and Melumad and Shibano (99). Authority, delegation and incentives: The role of decision rights has also been analyzed from other angles. Aghion and Tirole (997) show how delegation of a project choice decision can be used to motivate an agent to acquire information when the preferences of the principal and the agent are misaligned. Their model, however, takes the degree of incentive alignment as exogenous and the transmission of information is perfect. Rantakari (27b) examines how contracting di culties in uence the allocation of decision rights and how such di culties can be used to endogenize the degree of incentive con ict in Aghion and Tirole while leaving a role for delegation that is qualitatively di erent from monetary incentives. Still, Rantakari (27b) doesn t explicitly consider the process of communication. Dessein (22) illustrates how communication di culties encourage delegation by showing that the cost of biased decisions is typically lower than the costs of garbled information following strategic communication in the setting of Crawford and Sobel (982). In a setting with multiple decisions, Alonso (26) shows how sharing control of complementary decisions improves communication between an informed agent and an uninformed principal. With the exception of Rantakari (27b), the models take the degree of incentive alignment as exogenous. In contrast, the present paper shows how the degree of incentive con ict arises in equilibrium and how it depends on the current allocation of decision rights. Hierarchies: Organizational structures have also been analyzed from various other angles, but with the exception of the papers already mentioned, primarily only from a team-theoretic perspective. The paper closest to ours is Dessein and Santos (26), who examine a team-theoretic model that focuses on the limitations that the need for coordinated adaptation imposes on task specialization. Coordination in their model is, however, constrained only because information transmission is exogenously imperfect. Other perspectives include information processing (for example, Marshak 7

8 and Radner, 972, Bolton and Dewatripont, 994), problem-solving (for example, Garicano, 2), screening for interdependencies (Harris and Raviv, 22), managing asset utilization (Hart and Moore, 25) and coordination and experimentation (Qian, Ronald and Xu, 26). 3 The Model The basic structure of the model parallels the frameworks of Rantakari (27a) and Alonso, Dessein and Matouschek (26), with the addition of active information acquisition and the resulting endogenization of incentive provision. The organization consists of two divisions, i and j, that need to both respond to their local environments and coordinate with each other. Each division is headed by a division manager (local agents i and j, respectively), who must acquire information about their local conditions for decision-making purposes. In addition to the local agents, there exists headquarters (manager, M), who invests in purely productive e ort. If decisionmaking is decentralized, after information acquisition, the local agents communicate with each other through cheap talk after which they make decisions. If decisionmaking is centralized, they communicate through cheap talk with the manager, who then makes the decisions. 3. Payo structure Divisions: The organization consists of two divisions, i and j. Given the decision d i of how to run the operations of division i, the ex post pro t of division i is given by: i = K i i ( i d i ) 2 i (d j d i ) 2 + i f (e M i ) ; where i U i ; i indexes the locally optimal decision, with i and j independently distributed, and d j is the decision governing division j: We will refer to i ( i d i ) 2 as the adaptation component and to i (d j d i ) 2 as the coordination component of the pro t function, together comprising the decision-dependent part of the divisional pro t. In addition to the decisions, the pro tability of the division 8

9 depends on the attention devoted to the division by the headquarters, captured by the e ort component, i f (e M i ) ; where f (e M i ) : We assume that K i is large enough so that the organization is worth operating and to simplify notation, since maximizing pro t is the same as minimizing loss, we will focus on the loss formulation of L i = i ( r i ) ( i d i ) 2 + r i (d j d i ) 2 i f (e M i ) ; where we have simply normalized the decision-dependent part so that the relative importance of coordination (dependency) to division i is parameterized by r i 2 [; ] while the overall importance of decision-making to the division is captured by i = ( i + i ) : We assume that all monetary costs and bene ts of the organization are re ected in the pro t and loss accounts of the two divisions (and that these cannot be manipulated), so that the ex post performance of the organization is given simply by L i + L j : Local agents: The local agents contribute to the performance of their division by acquiring information about the local conditions to improve the quality of decisionmaking. In particular, the local agent i acquires a signal t i of the realized state i that is correct with probability p i and a random draw from U i ; i with probability p i at a personal cost (under governance structure g 2 fdec; centg) of C i (g; p i ) ; with C i;g p 2 i C i;cent p i (p i ) = to guarantee an interior solution and Cp i;dec i (p i ) (p i ) > and lim pi! Ci;g p i (p i ) to capture the idea that involvement in decision-making can decrease the e ciency of information acquisition due to time constraints or other reasons: The local agent doesn t learn whether the signal is correct or not, so that upon observing a signal t i ; his belief about the local state is given by E i ( i jt i ) = p i t i : The behavior of the local agents is managed through a pro t-sharing plan. In particular, while we assume that (p i ; i ; d i ) are not contractible, the pro tability of each division is veri able. In particular, agent i is o ered a linear incentive contract T i (L i ; L j ) = A i s i i L i s i j L j ; which is used to guide information acquisition, communication and, if given control, decision-making. The ex post utility of agent i is then given by U i = T i (L i ; L j ) C i;g (p i ) : 9

10 M M mi mj i j i mj mi j pi ti di dj tj pj pi ti di dj tj pj (A) Centralization (B) Decentralization Figure : Alternative governance structures Manager: In contrast to the local agents, the manager is unable to acquire information directly. However, she is able to contribute to the pro tability of division i by exerting productive e ort at a convex personal cost C M;g (e M i ; e M j ) ; with C M;g e M i e M j (e M i ; e M j ) : We also assume that C M;dec e M i (e M i ; e M j ) C M;cent e M i (e M i ; e M j ) to maintain the possibility of costly decision-making. As with the local agents, the manager also needs to be motivated through a pro t-sharing plan. o ered to the manager is given by T M (L i ; L j ) = A M s M i L i s M j L j ; The contract so that the ex post utility of the manager is given by U M = T M (L i ; L j ) C M;g (e M i ; e M j ) : 3.2 Timing of events and the choice of governance structure We will focus on analyzing two governance structures. Under centralization, both decisions are controlled by the manager. Under decentralization, the decisions are controlled by the respective local agents. These two governance structures are summarized in gure, depicting the ow of information. The timing of events is further detailed in gure 2 and is the same under each governance structure. First, each local agent invests p i in information acquisition and the manager exerts productive e ort (e M i ; e M j ) to maximize their respective expected payo s. The timing of managerial e ort is irrelevant to the analysis.

11 Local agents invest in information acquisition, the manager exerts productive effort Decisions are made Allocation of the decision rights and the incentive structure are chosen Local agents communicate with the decision maker(s) through one round of simultaneous cheap talk Payoffs are realized Figure 2: Timing of events Second, the local agents send non-veri able messages (m i ; m j ) about their local conditions to the decision-maker(s). In the case of centralization, this communication is vertical (to the manager), while in the case of decentralization it is horizontal (to the other local agent). Third, the decision-maker(s) use the received messages and any additional information they have available to choose decisions that again maximizes their respective payo s. contract. Fourth, payo s are realized and shared according to the The objective in the design stage is to choose an allocation of decision rights (a governance structure g 2 fdec; centg)and a pro t-sharing rule fs i ; s j g that maximizes the expected surplus generated by the game described. We assume that s i i +s j i +s M i ; so that the pro t stream of either division cannot be leveraged. Letting u be the identity of the decision-maker controlling d i,! g u the information available to the decision-maker u in the decision-making stage under governance structure g and fm g kg the nest incentive compatible partition of the cheap talk game under governance structure g between the decision-maker(s) and the local agent k, we can write the program as: min E (L i (d g ; e M ) + L j (d g ; e M )) + C M (e M ) + C i (p i ) + C j (p j ) g;fs i ;s j g s.t. m g k d g u 2 arg mine (s u i L i + s u j L j j! g u; g) ; u 2 fi; j; Mg d 2 arg mine s k i L i + s k j L j jd g i (mg k ; :) ; dg j (mg k ; :) ; t k ; k 2 fi; jg fm g kg p k 2 arg mine s k i L i + s k j L j jd g i (:) ; dg j (:) ; fmg i (t i)g ; m g j (t j) +C k;g (p) ; p k 2 fi; jg e M 2 arg mine (s M i L i + s M j L j ) + C M;g (e M ) ; e i ;e j where the constraints simply require incentive-compatibility in each stage of the game: (i) decisions are individually optimal to the decision-maker(s) given the information available to him or her, (ii) the messages sent are individually optimal to the local

12 agents given the structure of the communication equilibrium and the structure of the equilibrium decisions, (iii) information acquisition by the local agents is individually optimal given its expected nal impact on the equilibrium outcome, as given by the communication and decision equilibria, and (iv) the manager exerts an individually optimal level of productive e ort. In addition, the beliefs held by the participants at each stage of the game have to naturally be correct in equilibrium. 3.3 Preliminaries Because of the high dimensionality of the model, we will present the analysis in a number of steps. Section 4 derives the solution for the decision-dependent part of the loss under centralization and decentralization under the assumption of symmetric divisions ( i = j, r i = r j and i = j ) and a given degree of incentive alignment, adds information acquisition and e ort provision and discusses the choice of incentives. The general solution is summarized in Appendix A and discussed in detail in Rantakari (27a). In what follows, we will focus on information acquisition and incentive alignment at the expense of detailed discussion of communication and decision-making. The reader wanting a more detailed exposition of these to steps is encouraged to visit either Alonso, Dessein and Matouschek (26) or Rantakari (27a). Comparative analysis of these two solutions, maintaining the assumption of symmetry, is then performed in section 5. Appendix B extends the analysis to asymmetric divisions and discusses how asymmetric governance structures can be used to improve upon the symmetric structures analyzed in sections 4 and 5. 4 Solution In this section we will derive the solution under the two governance structures. If communication and decision-making were non-strategic, then the allocation of decision rights would be irrelevant and rst-best incentives to acquire information could be provided under both governance structures. However, when communication and decision-making are strategic, then the organization faces the challenge of minimizing the total distance to the rst-best outcome, as given by the losses arising from (i) 2

13 suboptimal acquisition of information, (ii) strategic communication and (iii) strategic decision-making. Sections 4. and 4.2 derive the equilibrium decisions and the quality of communication under centralization and decentralization. Section 4.3 presents the equilibrium expected losses and adds e ort provision and information acquisition to characterize the equilibrium choice of compensation structure. Section 4.4, which is the key to understanding the comparative static results of section 5 regarding the choice of governance structure, analyzes how the two governance structures di er in terms of returns to incentive alignment and true and perceived value of information. Finally, when the divisions are symmetric, the equilibrium sharing rule is symmetric. Thus, to simplify notation, let s M = s M i = s M j be the share of each division allocated to the manager; s = s i i = s j j the share of each division retained by their respective local agents and es = s i j = s j i the share of the other division allocated to the local agents. The degree of inter-divisional con ict is then measured by s=(s+es): 2 4. Equilibrium Decisions In the communication stage, the decision-maker(s) use the information available to them to make decisions that maximize their individual payo s. Under centralization, the manager is provided with an equal share of both divisions and thus makes pro tmaximizing decisions given the information available to him, independent of divisional incentives. Under decentralization, whenever s > es; the local agents place too much weight on the performance of their own division. This home-division bias leads to decisions that are under-coordinated with each division while excessively adapted to their own local conditions whenever the importance of coordination is interior. 4.. Centralization In the decision-making stage, the manager s information consists of messages m i and m j received from agents i and j regarding the observed signals t i and t j ; respectively. Thus, the manager solves 2 Of course, the true con ict depends on the underlying environment, but while interdependencies can be hard to measure, the amount of pro t-sharing is typically observable and hence we will focus on this slightly odd version of con ict. 3

14 min d i ;d j s M E (L i + L j jm i ; m j ) : Taking the rst-order conditions and solving them yields the pro t-maximizing decision rule d cent i = E M i +2rE M j +3r ; where E M i = p i E (t i jm i ) : However, the manager needs to rely solely on information communicated to her by the local agents. Thus, while the decisions themselves are appropriate given the information reaching the manager, the quality of information itself is endogenous and dependent on the degree of incentive alignment between the manager and the local agents and the incentives of the local agents to acquire information in the rst place Decentralization The solution under decentralization, where each local agent controls their respective decisions, parallels that of under centralization, with two di erences. First, in the decision-making stage, agent i knows his signal t i and his information thus consists of (i) the signal t i obtained regarding the realization of i ; (ii) the message m i sent to agent j regarding the realization of t i ; used by agent j to form beliefs about i s beliefs about i ; denoted E j E i i (= p i E (t i jm i ))and (iii) the message m j received from agent j regarding the realization of t j and used by agent i to form beliefs about j s beliefs about j ; denoted by E i E j j : Second, if s > es; decision-making will generally be biased relative to centralization because of the excessive weight placed by agent i on the pro tability of division i. Thus, agent i solves min d i E (sl i + esl j jt i ; m i ; m j ) and similarly for agent j: Solving the rst-order conditions yields a decision rule d dec i = s( r) s+esr E i i + (s+es)r ((s+esr)+r(s+es)) E ie j j + (s+es) 2 r 2 (s+esr)((s+esr)+r(s+es)) E je i i : Independent of the degree of incentive alignment, the equilibrium decisions converge to rst-best both when r! and when r! : In the rst case, no coordination is needed. In the second case, since the divisional payo s are fully dependent on coordination, the agents become willing to coordinate even absent any pro t-sharing. 4

15 However, whenever s > es and r is interior, the decisions exhibit too little coordination (and correspondingly, excessive adaptation) from the perspective of pro t maximization because of the presence of the own-division bias. The role of incentive alignment in the decision-making stage is immediate: as s! es; the quality of decision-making is monotonically improving and converges to pro t-maximizing when a balanced sharing rule of s = es is achieved. Since the initial bias in the decisions is largest in the region of intermediate r; the value of improved incentive alignment (from a decision-making perspective) is correspondingly highest in that region. 4.2 Equilibrium Communication In the communication stage, the local agents send strategically non-veri able messages about the realization of their local information to the decision-maker(s) in an attempt to induce more favorable decisions. Of course, in equilibrium such attempts are futile and lead only to a garbling of the transmitted information. However, how much garbling takes place depends on the allocation of decision rights, the importance of coordination and the degree of incentive alignment between the organizational participants. In particular, the quality of communication under centralization (vertical communication) is decreasing in the importance of coordination while the quality of communication under decentralization (horizontal communication) is increasing in the importance of coordination. Further, the quality of vertical communication is always higher than the quality of horizontal communication for any given degree of inter-divisional con ict and as the inter-divisional con ict converges to zero, communication becomes perfect under both governance structures Centralization In the case of centralization, agent i sends a non-veri able message m i to the manager in an attempt to get the manager to adapt with d i to E i ( i jt i ) and to accommodate this adaptation with d j to improve coordination. As shown in Rantakari (27a) and Alonso, Dessein and Matouschek (26), the most informative partition of the cheap-talk game can be characterized by a single parameter 5

16 ' cent i = s+esr r(s es) 2 [; ) ; which we will refer to as the quality of communication (by agent i under centralization). This parameter characterizes the coarseness of the partition. When ' g i! ; communication becomes binomial (above or below ex ante expectation) and when ' g i! ; communication becomes perfect. Note that under centralization, communication is perfect when r = ; since the manager simply replicates the ideal decisions of the local agents and thus no incentive con ict is present, and the quality of communication is monotonically decreasing in r whenever s > es as the importance of coordination grows, the manager becomes increasingly unresponsive to the (own-division biased) demands made by the local agents, thus increasing the degree of incentive con ict. The role of incentive alignment is immediate as pro t-sharing is increased, the local agents become increasingly aligned with the preferences of the manager (and so with the goal of pro t-maximization), thus decreasing the incentive con ict and increasing the quality of communication. As s! es; the preferences become perfectly aligned and communication becomes fully informative Decentralization The solution under decentralization follows similarly, with the exception that since agent i is in control of d i ; the only purpose of communication is now to induce accommodation from agent j: The quality of communication is given by ' dec i = r(s es)2 +ess(+3r) (s+esr)(s es) : Communication is binomial when r = and the quality of communication is monotonically improving in r : as coordination becomes more important, the local agents become increasingly accommodating, reducing the size of the incentive con ict and thus increasing the quality of communication. Also, as in the case of centralization, the quality of communication is improving in the amount of pro t-sharing and becomes perfect as s! es: Two results regarding the quality of communication under the two governance structures present themselves. First, ' dec i (s; es; r) < ' cent i (s; es; r) 8s > es and r < ; 6

17 since the relevant incentive con ict is always lower between the manager and the local agent than between the two local agents. 3 Second, ' dec i (s; es; r)! ' cent i (s; es; r) when r! ; since when the problem becomes one of pure coordination, the equilibrium decisions under the two governance structures converge. However, ' g i (s; es; r! ) < since con ict remains over the focal point of coordination as long as s > es: 4.3 Equilibrium Losses Having derived the equilibrium decisions d g i ; dg j ; the equilibrium quality of communication by the local agents ' g i ; 'g j and assuming for now that the quality of primary information is given by p g i ; pg j ; we can then solve for the decision-dependent component of the expected loss, which for division i is given by EL g i = g i p g i 2 i + p g j 2 j + i (p g i )2 2 i + g i i V ('g i ) pg i 2 i + g i j V 'g j p g j 2 j ; where g i ; g i i and g i j are coe cients that depend solely on the equilibrium decisions (and so on the degree of inter-divisional con ict and the governance structure), i = ( r) =3 captures the direct cost of inaccurate primary information and V (' g i ) = = (4 + 3'g i ) is a simple transformation of the quality of communication measuring the variance of beliefs about the underlying state between the sender and the receiver: V (' g i ) = 3E (E u (t i jm i ) t i ) 2 : Thus, not surprisingly, the similarity in the structure of the decision-making and communication equilibria across the governance structures translate into similarity in the structure of the expected loss. The rst line captures the expected loss if communication were perfect, with g i capturing the quality of decision-making and i capturing the cost of imperfect primary information. From our discussion of decision-making it is immediate that dec i cent i ; since decision-making is worse under decentralization. The second line captures the additional loss caused by inaccurate communication about either state. Note that for each state this loss is composed of two parts. V (' g i ) 3 Note that this result does not depend on the fact that the manager has intermediate preferences, but on the fact that the qualitative motives for communication are di erent under centralization. In particular, the di erence can be even more pronounced if the manager simply replicates the decisions made by the local agents. 7

18 measures how inaccurate the communication is, while g i i measures how damaging this inaccuracy is. Because decision-making under centralization is fully dependent on secondary (strategically communicated) information, accurate communication is always more valuable under centralization (when accounting for the impact on both cent divisions): V (' i ) dec V (' i ). 4 i i + cent j i i i + dec j i Finally, because the governance and incentive structures in uence how much any primary information impacts the nal performance, p g i will generally di er across governance structures. Let us now turn into endogenizing p g i : 4.3. E ort choices and equilibrium compensation Having derived how information travels through the organization after its generation, the local agents then face a simple maximization problem when choosing how much e ort to exert in acquiring information. Since the returns to primary information are linear in (p g i )2 ; to simplify the notation, we have the local agents choosing (p g i )2 : Thus, agent i solves min (p i ) 2sELg i + eselg j + Cg (p i ) ; which gives us the rst-order condition s i g i + g i i V ('g i ) 2 i es g j + g j i V ('g i ) = C i;g (p i ) 2 (p i ) ; which in turn is nothing but equating the perceived marginal value of information with its marginal cost. Note that i g i + g i i V ('g i ) > and g j + g j i V ('g i ) > : Thus, under both governance structures, the quality of primary information is increasing in s and decreasing in es: We will return to this the perceived value of information in the next subsection. At the same time, the manager chooses her e ort to maximize her payo. Since there is no point in wasting incentives, we have that s M = ( s es) and thus the e ort choice regarding each division is given by the rst-order condition 4 Note, however, that the equilibrium quality of communication, given the degree of pro t-sharing, is also higher under centralization. The value aspect dominates most of the time even at the equilibrium quality of communication. 8

19 ( s es) i f (e M i ) = C M;g e M i (e M ) : Thus, we can write the optimization problem as: Proposition Under both governance structures, the optimal compensation structure solves min s;es ELg i + ELg j X k f (e M k k ) + C M;g (e M ) + X k C k;g (p k ) s.t. s i g i + g i i V ('g i ) 2 i es g j + g j i V ('g i ) = C i;g (p (p i ) 2 i ) ; ( s es) i f (e M i ) = Ce M;g M i (e M ) 4.4 Value of incentive alignment and primary information Having derived the program that de nes the equilibrium compensation structure, we will now discuss the economic logic behind the choice of equilibrium strength of incentives. From above it is immediate that the organizational performance is increasing in the quality of primary information, communication and decision-making. Also, the quality of primary information is increasing in s and decreasing in es; while the converse is true for the quality of communication and, in the case of decentralization, decision-making. The question is then how the appropriate balance is determined. We will discuss the intuition in three steps. We begin by analyzing the true value of information, conditional on the degree of incentive alignment, which leads two basic results. First, the value of information is generally decreasing in the importance of coordination. Intuitively, the more important coordination is, the more constrained the decisions are, thus decreasing the value of information. Second, the value of primary information is naturally increasing in the degree of incentive alignment. In essence, strategic decision-making and communication are "leaks" that limit the value of information and which can be limited by increasing the degree of alignment. The smaller the leaks, the more valuable primary information is. We continue by analyzing the value of incentive alignment, conditional on the quality of primary information, which is in essence the converse of the true value of information. Intuitively, the lower the true value of information, the further away from 9

20 rst-best communication and decision-making the organization is and the more valuable additional pro t-sharing is. The analysis yields three intuitive results. First, the value of incentive alignment is generally increasing in the importance of coordination under both governance structures. Second, incentive alignment impacts communication and decision-making at di erent rates, causing the two governance structures to converge to the rst-best outcome at di erent rates. Finally, the value of incentive alignment is naturally increasing in the quality of primary information. We conclude by discussing the perceived value of information and what we call "free incentives." Whenever coordination carries positive value, any acquired information bene ts the division who performed the acquisition by improving the quality of adaptation while imposing a cost of accommodation on the other division. In consequence, full divisional ownership generates too strong incentives to acquire information and thus some incentive alignment can be achieved for free. This result is what we call free incentives and it is increasing in the importance of coordination. Also, not only does the true value of information depend on the governance structure, but so does the distribution of costs and bene ts of information, thus making the amount of free incentives dependent on the governance structure. The intuition behind the determination of the equilibrium compensation structure is then straightforward. First, utilize the free incentives to achieve rst-best information acquisition conditional on the resulting quality of communication and decisionmaking. Second, trade o the quality of primary information for improved transmission and use of information and managerial e ort until the margins are equated. The simple rule of thumb is that the less one needs to sacri ce the quality of primary information, the better the governance structure will perform True value of information From above, the true marginal value of information about i is given by " # MV g p i = i g i + g i i V ('g i ) () g j + g j i V ('g i ) where () measures the bene t to division i of more accurate primary information in terms of improved adaptation to local conditions and (2) measures the cost imposed on division j through the increased accommodation required by division j due to 2 (2) 2 i ;

21 the interdependence of the decisions. The comparative statics are summarized in the following proposition: Proposition 2 True value of information: (i) d d(s es) MV g p i (ii) d cent MV dr p i < ; d dec MV dr p i Q (iii) MV dec p i! MV cent p i when r!, r! and when s! es (iv) MV cent s s+es p i < x; then MV dec p i MV dec p i whenever r > r (s es) and s s+es x, MV cent p es) <. If These results are illustrated in gure 3. The intuition is straightforward: the value of information is constrained by two factors. First, the degree of interdependence impacts how much the decisions are able to respond to information, thus limiting its value. Second, strategic communication and, in the case of decentralization, decisionmaking, limit how well the primary information translates into nal decisions. In consequence, the value of information is increasing in the degree of incentive alignment, which limits the losses that occur between the generation of information and its nal impact on the organizational performance (part (i)). Part (ii) states that the value of information is generally decreasing in the importance of coordination under both governance structures. This result follows because, as mentioned above, when the divisions become increasingly interdependent, the less the decisions are able to adapt to local conditions. In addition, under centralization, the additional loss due to strategic communication is also increasing in the importance of coordination, leading to monotonically decreasing value of information. In the case of decentralization, the logic is the same, with the exception that the loss due to strategic communication and decision-making can be non-monotone in the importance of coordination when the degree of alignment is low, which can lead to a small region where the value of information is actually increasing in the importance of coordination. Part (iii) summarizes when the two governance structures are outcome equivalent, with the pro t-maximizing outcome achieved when r! and/or when s! es: Finally, part (iv) summarizes the di erence in the marginal value of information, which 2

22 MVcent MV dec MV cent MV dec r alignment r alignment r alignment (i) MV of information under centralization (ii) MV of information under decentralization (iii) Difference in the marginal value of information MV cent MV dec Figure 3: True marginal value of information in essence measures how well, given the degree of alignment and the importance of coordination, the governance structure uses that information. Whenever coordination is su ciently unimportant, then for all degrees of incentive alignment, the loss due to strategic communication under centralization is higher than the loss due to strategic communication and decision-making under decentralization and thus decentralization dominates. It is only when coordination is su ciently important and the degree of incentive alignment is su ciently low that the improvement in decisionmaking achieved under centralization dominates and information is more valuable under centralization. To understand this result better, we will now turn to analyzing the value of incentive alignment Value of incentive alignment The value of incentive alignment, conditional on the quality of information, is roughly the converse of the value of information, conditional on the degree of incentive alignment. High value of information (conditional on the importance of coordination) implies that the biases in equilibrium decisions are low and communication is accurate. Conversely, low value of information implies that the bias is high and/or communication is valuable and inaccurate. Thus, in broad terms, high value of information implies a low value of incentive alignment and vice versa. The quali er to this logic is that the marginal value of information is related to the absolute distance 22

23 to the rst-best outcome while the value of incentive alignment is determined by the marginal improvement. The two, however, are closely related. To analyze the returns to incentive alignment, recall that in the case of centralization, increasing the degree of pro t-sharing improves the quality of communication and thus the bene t is measured by MV(s cent es) = cent i i + cent j (' cent i es) p i i 2, while in the case of decentralization, increasing pro t-sharing improves both the quality of communication and decision-making, and is given by MV(s dec es) = dec i i + (' cent i ) j es) dec i + dec j ) es) Comparing the two components yields the following dec i i + dec j i) 2. V ' es) i p i i Proposition 3 Value of incentive alignment: (i) The value of incentive alignment is increasing in the quality of primary information. Holding the quality of primary of information constant, increasing the alignment of interests is always valuable and: (ii) d cent MV dr (s es) > and d dec MV dr (s es) R : (iii) d d(s cent MV es) (s es) < and d dec MV d(s es) (s es) R : (iv) MV(s dec cent es)! MV(s es) (v) MV(s dec cent es) > MV(s es) when r! and when r! : whenever r > r (s es) ; es) < Part (i) makes the obvious statement that the value of incentive alignment is increasing in the accuracy of information: the more information there is, the more valuable its accurate transmission is. The remainder of the proposition examines the 23