Collusion with intertemporal price dispersion

• DOI: http://doi.org/10.1111/1756-2171.12309
• Author: Vladimir Smirnov,Nicolas de Roos
• Published date: 01 March 2020
• Date: 01 March 2020

RAND Journal of Economics

Vol.51, No. 1, Spring 2020

pp. 158–188

Collusion with intertemporal price

dispersion

Nicolas de Roos∗

and

Vladimir Smirnov∗

We develop a theory of optimal collusive intertemporal price dispersion. Dispersion clouds

consumer price awareness, encouraging firms to coordinate on dispersed prices. Our theory

generates a collusive rationale for price cycles and sales. Patient firms can support optimal

collusion at the monopoly price. For less patient firms, monopoly prices must be punctuated with

fleeting sales. The most robust structure involves price cycles that resemble Edgeworth cycles.

Low consumer attentiveness enhances the effectiveness of price dispersion by reducing the payoff

to deviations involving price reductions. However, for sufficiently low attentiveness, price rises

are also a concern.

1. Introduction

The nagging presence of competitors is an inescapable fact of life for most firms. To

understand pricing behavior, wemust therefore consider the implications of repeated interaction.

The theory of repeated games offers some insights; notably, repeated play opens up opportunities

for punishments and rewards, permitting higher prices to be supported. However, nontrivial price

dynamics are also a common outcome of repeated play.For example, using scanner data covering

1.4 million goods in 54 geographic markets, Kaplan and Menzio (2015) find that close to half the

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

Weare grateful to Murali Agastya, Jim Albrecht, Mark Ar mstrong, Michelle Bergemann, SergeyIzmalkov, Eric Maskin,

Mark Melatos, Ariel Pakes,David Pearce, Debraj Rey, John Romalis, AbhijitSengupta, Kunal Sengupta, Andy Skrzypacz,

Juuso V¨

alim¨

aki, Jeroen van de Ven, Andrew Wait, and anonymous referees for useful comments, suggestions, and

encouragement. We thank attentive seminar audiences at the University of Bielefeld (2013), the Australian National

University (2013), the University of New South Wales (2013), the University of Sydney (2013), the University of

Queensland (2013), Georgetown University (2014), the Stern School of Business at NYU (2014), Harvard University

(2014), Boston College (2014), New York University(2014), the Free University of Amsterdam (2014), the University of

Amsterdam (2014), the University of Mannheim (2014), the University ofGroningen (2014), the New Economic School

(2016), and Monash University (2017).

158 C2020, The RAND Corporation.

DE ROOS AND SMIRNOV / 159

variation in prices is intertemporal.1An even larger role is typically played by intertemporal price

variation in retail gasoline markets subject to regular price cycles known as Edgeworth cycles.2

The rationale for these pricing patterns is not obvious in a repeated game setting. If the threat

of punishment is available, whydon’t firms employ it to support the highest feasible fixed price?

Complicated pricing patterns may be both more difficult to coordinate on and less profitable.

In this article, we develop a theory of coordinated price dispersion that provides an intuitive

explanation. Our theory rationalizes commonly observed pricing patterns including sales, price

cycles, and fixed prices. Our starting point is the consumer.

Pretend for a moment that you are a consumer. Think of a few products that may be in your

shopping basket; for example, milk, coffee, petrol, breakfast cereals. What is the current price of

these items at your local store? What is the current price at other stores? Would you recognize

a bargain? Your answers to these questions may vary by product; frequency of purchase and

prominence of display are obvious factors. We conjecture that the complexity of pricing patterns

also plays a role. A consumer who routinely observes a single price may become accustomed to

that price and recognize immediately a departure from this simple pricing pattern. By contrast,

complicated price paths are more difficult to absorb, making price changes less obvious.3If

consumer price perceptions are influenced by pricing patterns in this manner, they may be ripe

for manipulation by firms. We consider the optimal pricing problem of a cartel faced with

this prospect.

In our model, firms engage in repeated simultaneous price competition for a homogeneous

product. Weseek the optimal collusive pricing strategy.As with any cartel, the immediate problem

is to maintain incentives for internal discipline. Each cartel member trades off the short-term

incentive to deviate and raise current profits against the long-term benefit of receiving lucrative

cartel payoffs. We introduce imperfectly attentive consumers to this standard environment. The

premise of the model is that the set of prices each consumer is aware of depends on the recent

history of prices. Prices that are historically low are included in each consumer’s awareness set

for sure, whereas other prices are in the awareness set only with positive probability. Consumers

then choose the cheapest offering in their awareness set. This introduces a novel consideration

for the cartel. The cartel’s price path determines the prices consumers experience, giving the

cartel the ability to manipulate consumer awareness, with direct consequences for the incentive

constraints of the cartel. The optimal dynamic price path for the cartel emerges as a trade-off

between profitability and obfuscation.4

In addition to cartel manipulation, innate market characteristics influence a consumer’s

tendency to perceive and recall price information. We parameterize our model by the level of

consumer attentiveness, ranging from perfect awareness to complete inattentiveness. At one

extreme, our specification approaches the Bertrand model and obfuscation is futile. Consumers

are aware of all prices and an undercutting firm captures the whole market independent of the

1Kaplan and Menzio (2015) use the Kilts-Nielsen Consumer Panel Dataset, which records the shopping behavior

of approximately 50,000 consumers overthe period 2004–2009, and contains over 300 million transactions. The authors

decompose the variation in prices into that due to variation across stores, across products at a given store, and across

transactions over time for a specific product-store pair,finding that inter temporal variationin prices accounts for close to

half the variation.

2For example, in the Perth gasoline market studied byWang (2009) and de Roos and Katayama (2013), a similar

decomposition revealsthat in 2003, approximately 54% of the variation in retail margins is accounted for by intertemporal

variation in margins at a given retail station. If we condition onlyon stations par ticipating in the cycle (the majority of

stations), this rises to around 97%. Further details are available on request.

3This line of reasoning is supported by the concepts of rehearsal and associativenessthat Mullainathan (2002) draws

from the literature on memory research. Taken together,these two principles may imply a constant price would become

a well-established reference for comparison, whereas an intertemporally dispersed price path might be less amenable to

these memory processes.

4Throughout the article, we use the term obfuscation to refer to the cartel’s manipulation of consumer awareness

sets. This choice of language is in the spirit of Ellison and Ellison (2009), who use the term to refer to the manipulation

of rationally optimizing consumers subject to search frictions.

C

The RAND Corporation 2020.