RANDOM AUTHORITY

• DOI: http://doi.org/10.1111/iere.12214
• Published date: 01 February 2017
• Date: 01 February 2017

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 1, February 2017

RANDOM AUTHORITY∗

BYSIGUANG LIAND XIWENG1

Southwestern University of Finance and Economics, China; Peking University,China

This article rationalizes matrix management in a multiproject organization in which decisions must be adapted to

local conditions but also coordinated with each other. Project managers are privately informed about local conditions

and communicate strategically via cheap talk. Matrix management is modeled as a randomization over deterministic

authority allocations. We show that random authority is strictly optimal when the conflict between adaptation and

coordination is very severe or the coordination need is very small. Moreover, the optimal degree of delegation changes

nonmonotonically in the coordination need when the incentives of the project managers are sufficiently aligned.

1. INTRODUCTION

A central question for the internal organization of a firm is how to allocate authority within

its members.2The traditional unity-of-command principle of management suggests a clear and

single flow of authority from the top of an organization to its bottom. In practice, however, am-

biguity or randomness arises about who will be making certain decisions in matrix organizations,

due to their multiple manager structure.3For example, by investigating project management

in research and development (R&D) organizations, Goodman (1967) argues that “in the in-

dustry as a whole, the structuring of authority apparently has been random.” In this article,

we develop a model to study how random authority (RA) allocation affects an organization’s

overall performance and investigate when RA allocation outperforms deterministic authority

allocations.

We consider an organization with two project managers (“he”) and one functional manager

(“she”).4The interests of the functional manager and the two project managers are misaligned:

The functional manager’s objective is to maximize total profits, whereas each project manager

is biased toward maximizing the profits of his own project instead of those of the overall organi-

zation. To maximize profits, decisions must be adapted to local conditions but also coordinated

∗Manuscript received November 2013; revised September 2015.

1We would like to thank Hanming Fang (the editor) and four anonymous referees for comments and suggestions

that greatly improved the article. We thank numerous colleagues for insightful discussions and comments, in particular

Hongbin Cai, Wouter Dessein, Jan Eeckhout, Ehud Kalai, Ehud Lehrer, Jin Li, Qingmin Liu, Niko Matouschek,

Cheng-Zhong Qin, Yanlong Zhang, and Li-An Zhou. A summary of an early version of this article (Weng and Li, 2012)

was published in Operations Research Transactions (in Chinese). Weng acknowledges the financial support from the

National Natural Science Foundation of China (Grant No. 71303014) and Guanghua Leadership Institute (Grant No.

12-02). We also acknowledge support from Spanish Ministry of the Economy and Competitiveness (Project ECO2012-

36200) and Key Laboratory of Mathematical Economics and Quantitative Finance (Peking University), Ministry of

Education, China. Please address correspondence to: Xi, Weng, Guanghua School of Management, Peking University,

Beijing, China 100871. E-mail: wengxi125@gsm.pku.edu.cn.

2See Bolton and Dewatripont (2012) and Gibbons (2010) for excellent surveys of the literature on authority in

organizations.

3Discussions on matrix organizations can be found in Davis and Lawrence (1978), Ford and Randolph (1992),

Gottlieb (2007), and Knight (1976).

4A matrix organization typically has more than one functional manager. Our model can be viewed as a simplification

by assuming that the functional managers do not possess any private information, and there exists no coordination need

between the two functional managers. See related discussions in Section 5.

211

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(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

212 LI AND WENG

with each other. However, information about local conditions is held by project managers, and

this makes the strategic communication between these managers very important.5

Following the literature, we assume that the organization lacks commitment such that incen-

tive contracts cannot work. Therefore, the only way to provide communication incentives is

through authority allocation. We consider both deterministic and RA allocations in this article.

Specifically, we consider the following deterministic authority allocations: functional author-

ity, where decision rights are centralized to the functional manager; project authority, where

decision rights are delegated to project managers; and mixed authority, where the functional

manager controls one project, whereas the other one is delegated to another project manager.

RA involves a randomization of these deterministic authority allocations.6The game proceeds

as follows: First, the organization chooses authority allocation to maximize expected profits.

Second, after observing the authority allocation and information about local conditions, each

project manager sends a cheap-talk message to influence the posterior beliefs of the potential

decision maker(s) (henceforth DM). The message is observable by both the functional man-

ager and the other project manager. Finally, the DMs are chosen according to the committed

authority allocation, and the decisions are made based on the cheap-talk messages.

We characterize the communication equilibria given an authority allocation in symmetric

organizations, where the two projects are identical. Organizational performance is measured by

the total expected profits in the most efficient communication equilibrium. Allocating authority

to project managers has a natural advantage in terms of adapting decisions to local conditions,

since decisions are made by the managers with the best information about those conditions.

However, it also has a natural disadvantage in coordinating decisions. Therefore, the comparison

of organizational performance under different authority allocations crucially depends on two

parameters: incentive misalignment, which measures the biasedness of each project manager’s

incentives; and coordination need, which measures the relative importance of coordination in

the profit function.

Our main theoretical result suggests that randomization between functional authority and

project authority outperforms deterministic authority allocations under some parameter val-

ues. The optimal authority design depends on two factors: One is the relative importance of

adaptation compared with coordination, whereas the other is the communication quality. Com-

munication quality is the key reason for the optimality of RA. If communication quality does

not change with randomization probability, then there is no need to randomize: The optimal

authority allocation is either functional authority or project authority, depending on the relative

importance of adaptation compared with coordination. RA can be optimal because increasing

the probability assigned to functional authority improves communication quality due to the fact

that the project managers are more willing to share information with the functional manager,

as the interests of the functional manager are better aligned with those of the project manager.

Moreover, the gain in communication quality is a concave function of the probability assigned to

functional authority: As the probability goes up, the marginal improvement in communication

quality diminishes. This creates the possibility that at an interior probability, the marginal loss in

adaptation is equal to the marginal gain in communication quality, and hence the corresponding

RA maximizes the total expected profits.

RA is optimal in two scenarios. In one scenario whenever functional authority and project

authority perform equally well, RA is strictly optimal. Intuitively, this is when the conflict

5There is a growing literature investigating how the trade-off between adaptation and coordination affects the

delegation of authority in a strategic information transmission environment (e.g., Alonso et al., 2008, 2015; Dessein

et al., 2010; Friebel and Raith, 2010; Rantakari, 2008, 2013).

6In matrix organizations, RA can be implemented through the intervention of upper-level authority. As argued by

Knight (1976), the aim of the intervention is to “strike a balance between functional authority and project authority.”

Another way of implementing RA is from the result of joint bargaining between project managers and functional

managers. We can model this bargaining by letting the functional manager and one project manager simultaneously

send another message chosen from a suitable set of messages. These additional messages determine the allocation of

decision rights through a jointly controlled lottery following Aumann and Hart (2003) and Krishna and Morgan (2004).

As a result, authority allocation is de facto random with predetermined randomization probabilities.