Vertical relations, opportunism, and welfare

• Published date: 01 June 2019
• Date: 01 June 2019
• Author: Germain Gaudin
• DOI: http://doi.org/10.1111/1756-2171.12272

RAND Journal of Economics

Vol.50, No. 2, Summer 2019

pp. 342–358

Vertical relations, opportunism, and welfare

Germain Gaudin∗

This article revisits the opportunism problem faced by an upstream monopolist contracting

with several retailers over secret agreements, when contracts are linear. We characterize the

equilibrium under secret contracts and compare it to that under public contracts in a setting

allowing for general formsof demand and retail competition. Market distortions are more severe

under secret contracts if and only if retailers’ instruments are strategic complements. We also

investigate the effect of opportunism on firms’ profits. Our results remain robustwhether retailers

hold passive or wary beliefs. We derive some implications for the antitrust analysis of information

exchange between firms.

1. Introduction

When an upstream firm secretly contracts with downstream retailers, an opportunism prob-

lem may arise. The upstream firm may have an incentive to deviate from the offers it would make

if contracts were observable by every retailer.1For instance, when secret agreements are over

two-part tariffs and retailers hold passive beliefs about what their competitors are offered, the

upstream firm will sell its input at cost and capture the entire downstream profit through fixed

fees, thus earning less than the monopoly profit it could achieve if contracts were public. This

result was first shown by Hart and Tirole (1990), O’Brien and Shaffer (1992), and McAfee and

Schwartz (1994). Opportunism lowers the retail price in this setting, as consumers always pay

less than the monopoly price at which they would purchase final goods if contracts were public.

These results, however, are specific to the case of efficient, nonlinear contracts where retailers

make a side payment to the upstream firm upon accepting an offer.In practice, distortive contracts

are widely used in many industries. Forinstance, linear contracts are common in relations between

(electronic-) book publishers and retailers (see, e.g., Gilbert, 2015), in negotiations between cable

TV distributors and channels (e.g., Crawford and Yur ukoglu, 2012, Crawford et al., 2018), in

∗European Commission (Directorate-General for Competition), and TelecomParisTech; germain.gaudin@ec.europa.eu.

I am grateful to the Editor, Mark Armstrong, and twoanonymous referees for their very useful comments and suggestions.

I also thank Marius Schwartz for his invaluablediscussion and advice, as well as Hans-Theo Normann, Markus Reisinger,

Emanuele Tarantino, Tim Thomes, and Christian Wey. The views expressed in this article are personal and do not

necessarily represent those of the European Commission.

1In this regard,this opportunism problem is analogue to that faced by a firm selling durable goods to final consumers;

see the seminal contribution by Coase (1972).

342 C2019, The RAND Corporation.

GAUDIN / 343

hospital-insurer relationships (e.g., Ho and Lee, 2017), or between hospitals and manufacturers

of medical devices (Grennan, 2013; 2014).2

In this article, we investigate the opportunism problem when an upstream firm and several

retailers bilaterally set linear contracts which only specify a per-unit price quote for the input. We

assume that either (i) it is common industry practice to use linear contracts, (ii) firms find it too

costly to implement nonlinear contracts, or (iii) linear contracts are enforced through regulation

or competition policy.3

We characterize the equilibrium under a general demand system when contracts are secret

and retailers hold passive beliefs, and we compare it to that under public contracts. Both settings

lead to some double-marginalization because of the distortive nature of linear contracts. We find

that secret contracts force the upstream monopolist to lower the input price (as compared to that

under public contracts) if and only if retailers’ instruments are strategic substitutes. By contrast,

both wholesale and retail prices are higher under secret contracts when retailers’ instruments are

strategic complements (which is a typical situation when retailers compete in prices). This result

cannot occur with efficient, nonlinear contracts under which secret offers always lead to lower

prices than public offers.

The intuition is as follows. Starting from the equilibrium input price levels under public

contracts, with secret contracts, the upstream monopolist has a unilateral incentive to increase

(respectively, to decrease) its input price to retailer iwhen the pass-through rate of this input

price to retail prices is lower (resp., greater) than under public contracts. Indeed, in that case, the

monopolist would benefit from such a unilateral move because an increase (resp., decrease) in its

markup on inputs sold to retailer iwould have a limited negative (resp., large positive) impact

on total input purchases. In this article, we show that this ranking of the retail pass-through rates

simply corresponds to retailers’ instruments being strategic complements (resp., substitutes).

We derive the implications of this result in ter ms of surplus and firms’ profits. In addition,

we also investigate the role of retailers’ beliefs. When retailers hold wary beliefs and compete

in quantities, the equilibrium is equivalent to that under passive beliefs. When they compete in

prices, however, the manufacturer has a direct incentive to adjust the offers made to all competing

retailers when deviating with one of them. If retailers are able to anticipate the manufacturer’s

incentives, wary beliefs thus appear more plausible than passivebeliefs. Under price competition

when retailers hold wary beliefs, we show that strategic complementarity is again equivalent to

prices being higher under secret contracts than public ones. Our main results are thus robust both

to retailers holding passive or wary beliefs and to competition being in price or quantity. We also

determine the key variables for comparing equilibrium prices under passive and wary beliefs.

These results have important implications for the antitrust analysis of information exchange

between firms. Indeed, theyimply that a public authority with a focus on consumer surplus should

prevent or allow retailers to exchange information related to their supply conditions depending

on whether their instruments are strategic substitutes or complements. Moreover, a laissez-faire

situation where retailers exchange cost-related information would Pareto-dominate, preventing

such exchange in standard models of price competition.

Related literature. The literature addressing the opportunism problem originated from the

analysis of efficient contracts (see Hart and Tirole, 1990; O’Brien and Shaffer, 1992; McAfee

2Linear contracts are also popular in (formerly) regulated network industries such as telecommunications, for

pricing access to an essential input, in particular, when a vertically integrated incumbent supplies to downstream rivals.

In such setting, the form of the wholesale contract is key in determining the incumbent’sstrategic incentives, as shown by

Moresi and Schwartz (2017). In addition, vertical contracts are generally assumed to be linear in the literature on input

price discrimination; see, for example, the work of DeGraba (1990), and Inderst and Valletti (2009).

3Taking the example of the retailing industry, Dobson and Waterson (2007) also argue that linear contracts could

be justified by the fact that negotiations between vertically related firms typically occur infrequently (e.g., annually),

especially when compared to retailers’ orders, which take place on a daily or weekly basis in order to adjust to demand,

inventory issues, or other exogenous shocks.

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