Collusion with limited product comparability

• Author: Nicolas Roos
• DOI: http://doi.org/10.1111/1756-2171.12242
• Published date: 01 September 2018
• Date: 01 September 2018

RAND Journal of Economics

Vol.49, No. 3, Fall 2018

pp. 481–503

Collusion with limited product comparability

Nicolas de Roos∗

Weexamine the effect of limited product comparability on the viability of collusion. Firms choose

messages to influence consumer product comparison. The cartel hinders transparency on the

equilibrium path and seeks it for optimal punishment. Five conditions are each sufficient to

ensure obfuscation aids collusion: if firms can mix over messages or commit to messages, if

messages are informative,or if an individual firm or the cartel can control comparability. We also

analyze the impact of message differentiation and complexity for optimal messages, and identify

a key role for the convexity or concavity of comparison probabilities in these features.

1. Introduction

The task faced by the consumer in a standard market setting is Herculean, involving the

evaluation and comparison of a vast array of multidimensional products. Decisions made by

firms often complicate this task. For example, competing retail products may display different

units of measurement for prices or quantities; headline airfares may omit additional charges

relating to baggage, seat selection, credit card fees, and taxes; mobile phone plans, insurance

contracts, and credit cards incorporate contingencies that are difficult to assess; the compatibility

of electronic goods with complementary products may be hard to evaluate; and firms may even

make exaggerated or inaccurate claims about their products. It is not surprising that consumers

are sometimes unable to compare all available products, a fact long appreciated bymarketers and

regulators (Piccione and Spiegler, 2012).

A consumer faced with a product choice complicated by the decisions made by competing

firms could be forgiven for suspecting a conspiracy to soften market competition. To date, a

growing literature on obfuscation in oligopoly has presumed the opposite.1Rather than examine

the collective incentive for obfuscation, the literature has focused on the unilateral incentive of

each firm to obfuscate. Given that repeated interaction is the norm in oligopoly, this omission

is surprising. The logic is articulated concisely by Ellison and Wolitzky (2012): “Why collude

∗University of Sydney; nicolas.deroos@sydney.edu.au.

I am grateful to Murali Agastya, Mark Armstrong, Simona Fabrizi,Steffen Lippert, Jonathan Newton, Kunal Sengupta, and

Jidong Zhou; two anonymous referees; participants at the Australasian Economic Theory Workshop(Monash University,

2016), the University of Queensland Industrial Organisation Workshop(2016), the Asia-Pacific Industrial Organisation

Conference (University of Melbourne, 2016), the Conference of the European Association for Research in Industrial

Economics (Maastricht University, 2017), the conference of the Mannheim Centre for Competition and Innovation

(2018); and seminar audiences at the University of Giessen (2017) and the University of D¨

usseldorf (2017) for valuable

comments and encouragement.

1See Spiegler (2016) and Grubb (2015) for recent discussions of related literature.

C2018, The RAND Corporation. 481

482 / THE RAND JOURNAL OF ECONOMICS

on obfuscation rather than just colluding on price?” In this article, we provide a simple answer.

Coordinating on obfuscation may relax the incentive constraints of a cartel, enabling effective

collusion on price.

Weadapt the consumer choice framework of Spiegler (2016), in which obfuscation operates

through limited product comparability, to examine the coordination problem of a price-fixing

cartel with opportunities for obfuscation. This framework has the virtue that it can illustrate a

range of models of obfuscation, including the manipulation of product description formats (Carlin,

2009; Piccione and Spiegler, 2012; Chioveanu and Zhou, 2013), the emphasis or shrouding of

product attributes (Gabaix and Laibson, 2006), and consumer search (Varian,1980). We examine

the conditions under which collusion is aided by obfuscation, and the optimal form of obfuscation

for the cartel.

In our model, nfirms simultaneously choose a price and a “marketing message” for a

homogeneous product overan infinite horizon.2Marketing messages are broadly defined to include

any aspect of the marketing or description of a product that may influence consumer product

comparison, including the units of measurement, the specification of contingencies, or even the

language or jargon employed byfir ms to frame their products. The vector of marketingmessages

stochastically influences the propensity of consumers to make binary product comparisons.

A product is eliminated from the consumer choice set only if there is a cheaper comparable

alternative. Thus, the message vector affectsconsumer choice by influencing the set of comparable

product pairs.

The fundamental problem for any cartel is to maintain internal incentives for cooperation.

The cartel’s incentive constraints depend on the collusive profits promised by cartel policies,

the profits available to a firm deviating from cartel policies, and the severity of punishment the

cartel is able to inflict on a deviator. Limited comparability introduces a trade-off by impacting

both deviation and punishment payoffs. The cartel can manipulate this trade-off through careful

message choice. A deviation involving marginallyundercutting the cartel price is more profitable

the greater the number of comparable products. Cartel members therefore have an incentive to

limit the transparency of the message profile on the equilibrium path to minimize the possible

gains to deviation. By contrast, the severity of punishment depends on the ability of the cartel to

reconfigure the message vector to facilitate product comparison. A deviating firm has the opposite

incentives,and therefore the choice of messages can be framed as a battle for t ransparencybetween

a deviator and the remaining cartel members.

In the battle for transparency, several factors tilt the balance of power between deviator and

cartel, and thus determine the critical discount factor of the cartel. First, the deviator has an

advantage as a Stackelberg follower: she has an opportunity to respond to the equilibrium path

messages of the cartel. Thus, despite our focus on simultaneous play, it is as if a deviator moves

second. The deviator enjoys a similar privileged position for the purposes of punishment. If this

advantage can be neutralized, then limited comparability is weakly beneficial to the cartel. We

establish a number of separate conditions which do exactly that. If mixedstrategies are available,

if the cartel can commit to messages, or if any firm or the cartel as a whole is able to control

comparability, then limited comparability is weakly beneficial.

Second, there is an asymmetry in the trade-off between deviation and punishment payoffs.

A single comparable product eliminates punishment payoffs, whereas complete comparability is

needed to maximize deviation profits. In the special case where either all products or no products

are comparable, the trade-off balances and, providing the Stackelberg follower advantage of

the deviator can be neutralized, the sustainability of collusion matches a perfect information

benchmark. This result applies directly to well-known models of consumer search. In the model

of sales of Varian (1980), consumers are either perfectly informed or completely uninformed

about prices; the sustainability of collusion is thus identical to the benchmark. This result also

explains a sharp distinction between two-firm cartels and larger cartels. With twofir ms, it follows

2Webor rowthis ter minologyfrom Spiegler (2014).

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