Equilibrium Principal‐Agent Contracts: Competition and R&D Incentives

• Published date: 01 September 2013
• Author: Michela Cella,Federico Etro
• DOI: http://doi.org/10.1111/jems.12021
• Date: 01 September 2013

Equilibrium Principal-Agent Contracts:

Competition and R&D Incentives

FEDERICO ETRO

University of Venice

Ca’ Foscari

federicoetro@yahoo.it

MICHELA CELLA

University of Milan

Bicocca

michela.cella@unimib.it

We analyze competition between firms engaged in R&D activities and market competition to

study the choice of the incentive contracts for managers with hidden productivity. Oligopolistic

screening requires extra effort/investment from the most productive managers: under additional

assumptions on the hazard rate of the distribution of types we obtain no distortion in the middle

rather than at the top. The equilibrium contracts are characterized by effort differentials between

(any) two types always increasing with the number of firms, suggesting a positive relation

between competition and high-powered incentives. An inverted U curve between competition

and absolute investments can emerge for the most productive managers.

1. Introduction

A wide literature on contract theory has described how asymmetric information shapes

the optimal contracts between a principal and an agent with private information. For

instance, when the agent is the manager of a monopolistic firm and has private infor-

mation on the productivity of effort, the optimal contract requires the first best effort for

the most productive type and a downward distortion of effort for all the less productive

types, with effort differentials associated with wage differentials in a way that insures

incentive compatibility (see Stiglitz, 1977 or Baron and Myerson, 1982). However,when a

firm is not a monopolist, but competes in the market with other firms, we can expect that

the optimal contracts are affected by competition and the competitive prices are affected

by the contracts implemented by all the firms. Although the analysis of equilibrium

principal–agent contracts has been studied in models with perfect competition [see Roth-

schild and Stiglitz (1976), or more recently, Bisin and Gottardi (2006) and Pouyet et al.

(2008)], there is limited work for the general case of imperfect competition. The notable

exception of Martimort (1996) examines equilibrium contracts in a duopoly where the

types of managers of the firms are perfectly correlated: this is a reasonable assumption

in the presence of common aggregate shocks, but not in the presence of firm-specific

shocks or asymmetric information on the productivity of the managers. We augment

principal–agent models between firms competing in the market and their managers

We are grateful to Hongbin Cai, Jacques Cremer, Martin Cripps, Jeoren Hinloopen, Eugen Kovac, Daniel

Kr¨

ahmer, Matthias Kr¨

akel, Konrad Mierendorff, Piergiovanna Natale, Patrick Rey, Urs Schweizer, and par-

ticipants at seminars at the Peking University, University of Bonn, University of Amsterdam, and Cresse

conference in Crete for discussions on the topic.

C2013 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume22, Number 3, Fall 2013, 488–512

Competition and R&D Incentives 489

with idiosyncratic and uncorrelated shocks that give raise to equilibrium contracts that

differ from those offered by a monopolistic firm. The aim is to investigate how entry in

a market affects the equilibrium contracts and, in turn, how these contracts affect the

endogenous market structure.

We consider firms that in a first stage choose contracts for their managers and in

a second stage compete in the market. Each contract provides incentives to undertake

R&D activities that reduce the marginal cost. At the time of competing `

alaCournot in

the last stage, the contracts or the cost-reducing activity become observable in our base-

line model. The interesting interaction occurs at the initial contractual stage between

the firms and their managers. The managers are ex ante homogenous but, after being

matched with a firm, they differ in their productivities, which are identically and inde-

pendently distributed. Weconsider as a benchmark case the one in which productivities

can be observed by the firm’s owner (but not by the rival), and then we consider the

more realistic situation in which each productivity level is private information to each

manager. The contracts are expressed in terms of effort/wage schedules. Our focus is

on Bayesian Nash competition in contracts: these are chosen simultaneously, taking as

given the contracts offered by the other firms.

The equilibrium principal–agent contracts require extra effort from the most pro-

ductive managers compared to the equilibrium contracts emerging with symmetric

information. This deviation from the traditional property of “no distortion at the top”

emerges because of the strategic interactions between contracts for different types (due

to strategic substitutability between efforts). In particular, the fact that all the competi-

tors commit to distort downward the effort of their inefficient managers increases the

marginal profitability of the effort of an efficient manager (likely to compete with in-

efficient ones), and vice versa. This enhances the polarization of the efforts required

from different managers. Under additional assumptions on the hazard rate of the dis-

tribution of types (which must be positive enough) we actually obtain “no distortion

in the middle”: all the best (worst) types exert more (less) effort than under symmetric

information.

Our main result on the relation between competition and incentives is the follow-

ing: the effort differential between (any) two types of managers is always increasing in

the number of firms, which may suggest a positive relation between competition and

high-powered incentive schemes. Loosely speaking, competition enhances meritocracy:

when the number of firms increases, each firm tends to differentiate more its contracts

(i.e., spend relatively more on wages for the best managers), requiring a relativelyhigher

effort from an efficient manager because this can lead to larger gains against less effi-

cient rivals. Also the absolute effort levels can increase with the number of firms, but

only for the most efficient managers: moreover, we show that in such a case an inverted

U curve between competition and absolute investment in cost-reducing activities can

emerge.

A wide industrial organization literature, started by Dasgupta and Stiglitz (1980),

Tan do n (1984), and Sutton (1991) and generalized in recent work by Vives (2008), has

studied the impact of competition on deterministic cost-reduction activities, showing

that an increase in the number of homogenous firms tends to reduce production, profits,

and investment of each firm. Our model generalizes this framework with heterogeneity

and uncertainty in firms’ productivity and also asymmetric information between firms’

owners and their managers engaged in the cost-reducing activities. Following the cited

literature, we also consider the case of endogenous market structures, that emphasizes

a positive relation between market size and relative (and possibly absolute) measures of