OFT Roundtable on Conjectural Variations
Introduction and Coordinated Effects
Adrian Majumdar
Adrian.Majumdar@rbbecon.com
Contributors
Adrian Majumdar
Benoît Durand
Chris Doyle
Alan Crawford
•
We are indebted to Greg Shaffer for his invaluable comments and
contributions to Chapters 2 and 5 and to Glen Weyl for his detailed and
insightful comments on Chapter 4.
•
We have benefited substantially from comments from Matthew Bennett,
Katie Curry, Stephen Davies, Peter Davis, Amelia Fletcher, Sonia Jaffe, KaiUwe Kuhn, Boryana Miteva, João Santos Silva, Ian Small, Frank Verboven,
Chris Walters and from participants at an OFT Roundtable and an OFT
seminar to discuss this report.
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Outline of the report / Terms of reference

Introduction
– What are CVs and how is their use justified?

A backward-looking approach
–

A forward-looking approach
–

Can empirical techniques use CV models to tell us anything about how firms
competed in the past?
Can CVs be used by policy makers, particularly with respect to unilateral effects
analysis in merger control in pricing pressure tests?
A broader perspective on firms’ reactions
–
In the spirit of CVs, what are the implications of modelling how firms react to
changes in their rivals’ actions for coordinated effects?
–
In light of this, to what extent should the Airtours criteria be revised…e.g. to include
“parallel accommodating conduct” as per the US guidelines?
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1. What are conjectural variations?
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1. What are Conjectural Variations?

Conjectural variations capture the expectation a firm has about how its rivals will react
when it changes its quantity or price.

Impact of conjecture on the intensity of competition

–
Benchmark is zero (standard approach in one-shot simultaneous move game)
–
Negative conjectures intensify competition (i.e. a reduction of output by one firm is
conjectured to be met with an increase in output of other firms).
–
Positive conjectures dampen competition (i.e. a reduction in output of one firm is
conjectured to lead to a reduction in output of other firms)
Example: quantity setting duopolists: CV = -1, 0, 1 => perfect competition, Cournot,
perfect collusion
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2. Selective summary of the literature on CVs
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2. A brief summary of the literature

Theoretically awkward (firms cannot react in a one-shot game)

Short cut to a more complex game with responses by rivals?

Yes – CV use of parameters allows replication of outcomes… but multiple equilibria

Consistent conjectures narrow down equilibria? Evolutionary stable? Reachable with
boundedly rational agents?

Possibly – but might not have equilibrium at all… and may still fail to capture underlying
game

CV parameters… useful concept for applied work – compare market outcomes against
CV=0 benchmark… “as if” firms behaved with those conjectures.

Where do conjectures come from? Short-cut to modelling outcome is silent on cause of
outcome
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3. A broader perspective on CV models
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3. A broader perspective: layout

A broader perspective:
–


In the spirit of CV’s, what are the implications of modelling how firms react to
changes in their rivals’ actions for coordinated effects?
Summarising the literature (selectively chosen to meet OFT ToR)
1.
Continuous punishment strategies
2.
Speed of punishment
3.
Alternating move models can give rise to stable, high-price equilibria
Policy issues:
–
In light of the literature, to what extent should the so-called Airtours criteria be
revised?
–
Does the CV literature motivate “parallel accommodating conduct” (mooted in the
US horizontal merger guidelines) as a coordinated effects theory of harm in merger
cases?
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3. A broader perspective: should the Airtours criteria be revised?


–
Coordinated effects (Merger Assessment Guidelines) :
1.
firms need to be able to reach and monitor the terms of coordination;
2.
coordination needs to be internally sustainable among the coordinating group; in
particular there must be adequate deterrents to ensure there is no incentive to
deviate from the agreement; and
3.
coordination needs to be externally sustainable, in that there is little likelihood of
coordination being undermined by competition from outside the coordinating group.
Similarly, the Airtours criteria:
1.
Alignment
2.
Internal stability (monitoring and punishment)
3.
External stability
The report focuses on criteria 1 and 2
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3. A broader perspective: textbook treatment of coordination
•
Textbook treatment: threat of ‘punishment’ must outweigh gain from ‘cheating’
‘Cheating’
Phase
‘Punishment’ Phase
Payoff
Gain to cheating
Impact of punishment
Detection Lag
Payoff under
coordination
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3. A broader perspective: responding to rival’s actions

Continuous punishment strategies
–
Does the “punishment fit the crime”? (Friedman and Samuelson (1994))
–
–
arguably more “realistic” to assume that firms react more to greater deviations
from an agreement, so that the size of the punishment increases with the
magnitude of the deviation.
Lu and Wright (2010): continuous punishment strategies in the form of pricematching punishments – if firm 1 lowers its price, then firm 2 will match that price
(within certain bounds)
–
Better scope for alignment with simple punishments (easier to communicate)?
–
Less harmful collusive outcomes (softer punishment)?
–
Coordination may be less likely to entirely break down than previously thought,
as following a deviation firms may still carry on coordinating, simply to a lesser
extent
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3. A broader perspective: responding to rival’s actions

Speed of punishment
–
Instantaneous price matching
–
Deviation profit ruled out by assumption?
–
More effective punishment strategies and therefore more stable coordinated
outcomes
–
Multiple (high price) equilibria with instant price-matching – monopoly outcome
focal only with symmetry (Hviid and Shaffer, 1999). Sufficient asymmetry gives
rise to competitive outcome.
–
Kinked-demand curve theories (with implicit pre-play communication, Bhaskar,
1988). If firm i undercuts j, j can undercut i. The pre-play stops when no-one
undercuts. Then sales are made at those prices. Symmetry => monopoly;
asymmetry => Stackelberg.
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3. A broader perspective: responding to rival’s actions

Alternating move models and supra-competitive prices
– Firms commit to a certain action and rivals may be able to respond while the firm is
still committed. Implications for competitive effects if this is how firm’s behave?
– Markov strategies – respond only to rival’s last action, not history of actions.
“Cheating” matters only if occurs in last period.
– Maskin and Tirole (1988b) show that stable high price equilibria may emerge from
alternating move games:
“... the strategies in the supergame literature typically have a firm reacting not only
to other firms but to what it did itself. By contrast, a Markov strategy has a firm
condition its action only on the other firms' behaviour. Thus, in a price war, a firm
cuts its price not to punish its competitor (which would involve keeping track of its
own past behaviour as well as that of the competitor) but simply to regain market
share. It strikes us that these straightforward Markov reactions often resemble the
informal concept of reaction stressed in the traditional I.O. discussion of business
behaviour (e.g., the kinked demand story) more closely than do their supergame
counterparts".
– I rationally anticipate my attempts to gain market share will be met aggressively by
you (without us coordinating at all).
– Extensions involve multiple equilibria. Edgeworth cycles too – depends on discount
factor.
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3. A broader perspective: what is the competitive outcome?

–
–
Concept 1: What is the competitive level?
One-shot outcome?
–
Even absent conjectures there is a distinction between textbook “collusion” and
collusion recognised by Authorities and courts.
–
Textbook: one penny above the one-shot price sustained in a repeated game is
collusion!
The most consumer friendly equilibrium of all possible equilibria?
–
But multiple equilibria are common
–
How does the system end up at a high-price equilibrium?
–
Shocks? Not anti-competitive – but is this a competitive outcome?
–
Focal points – how common are they?
–
Communication? May be anti-competitive.
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3. A broader perspective: what is the competitive outcome?

Concept 2: do accommodating conjectures imply coordination?
–
If firms take into account the responses of their rivals, they may well set higher prices
than if they took a short term view and ignored these reactions
–
But this does not itself imply that there is any form of anti-competitive behaviour, or what
Authorities might reasonably consider to be coordination in practice
–
–
Why should firms be expected to behave as if they did not take into account their
rivals’ responses – is this a realistic benchmark?
–
A firm having a conjecture as to how its rivals will respond is not anti-competitive in
and of itself
–
A key question: how were those conjectures formed?
Arguably there is a distinction between the outcome ultimately obtained, and the
manner in which it was arrived at
–
Simply being aware of rival responses and rationally anticipating them (not
coordination?)
–
Seeking to shape rivals’ reactions to make them accommodating (coordination?)
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3. A broader perspective: what is the competitive outcome?

Concept 3: impact of a merger in the presence of accommodating conjectures
–
Conjectures remain constant? “Unilateral effect”? See Jaffe and Weyl (2011)
–
Conjectures change to become more accommodating? “Coordinated effect?”
–
But why do they change?
–
–
New focal point arises (not necessarily “coordinated”)
–
Communication among firms is more likely / more effective at moving system to
high-price equilibria (coordinated)
Is there something in between a coordinated effect and a unilateral effect… or is that
distinction too simplistic?
–
Joe Farrell: mergers can be harmful without neatly falling into the standard
categories
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3. A broader perspective: should the Airtours criteria be revised?



Criterion 1: Alignment is under-researched – but important.
–
How to commit to price matching? Contractual? Pre-play communication?
Need for symmetry for the most harmful outcomes.
–
Multiple equilibria plague this literature! Symmetry matters to appeal to Pareto
dominance of monopoly outcome?
Criterion 2: Current criteria already address monitoring and punishment…
–
Current approach encompasses both continuous and instantaneous
punishments
–
Coordination can – in theory at least – be supported where “the punishment fits
the crime”.
–
Re-affirms the current approach that places substantial importance on
monitoring (pre-requirement of rapid reaction).
Criterion 3: External stability. Not discussed – but important.
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3. A broader perspective: where does ‘parallel
accommodating conduct’ fit in?

US Merger guidelines, coordinated effects section
“Parallel accommodating conduct includes situations in which each rival’s response to
competitive moves made by others is individually rational, and not motivated by retaliation or
deterrence nor intended to sustain an agreed-upon market outcome, but nevertheless
emboldens price increases and weakens competitive incentives to reduce prices or offer
customers better terms.”


Link to theory?
–
Focal point equilibria with Markov strategies (Maskin and Tirole, 1988b)?
–
Accommodating conjectures?
–
Can we measure / predict changes in conjectures caused by merger if we do not
understand where the conjectures come from in the first place?
–
When does a merger cause or strengthen this parallel accommodating conduct?
We do not deny the possibility of a harmful merger that is not clearly a unilateral or coordinated
effects case, but do not consider theory and practice to offer robust guidance on when these
mergers are most likely to occur or how often such “in between” cases would fail to be caught –
we would not advocate extending the Airtours criteria for the assessment of coordinated effects.
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