price caps as welfare-enhancing coopetition · 12th cresse conference heraklion, 2 july 2017 . 1...
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Price caps as welfare-enhancing coopetition
Patrick Rey and Jean Tirole
12th CRESSE conference
Heraklion, 2 July 2017
1
INTRODUCTION (1/3)
Coopetition: agreements among potential competitors
Major antitrust concern since Sherman Act: Cartels, but also
• Mergers
• Joint marketing agreements – Patent pools
– Alliances (airlines, code-sharing)
• Platforms – Health-care (HMOs)
– Content (cable/broadband/satellite operators)
– Shopping malls
Key aspect: complements or substitutes?
2
INTRODUCTION (2/3)
Complements versus substitutes
Heterogeneous (Qantas / China Eastern)
Moving (products and usage evolve over time)
Duality for platforms
• Cooperate to attract users to the platform
• Compete for users within the platform
→ screening whether such agreements lessen competition and harm consumers is information intensive
→ authorities often (understandably) hesitant to approve
3
INTRODUCTION (3/3)
Objective: add “information-free” instrument
Firms
Agree on price caps for their products
Keep control over their products (in contrast to mergers or old-style patent pools)
Intuition
Complements: solve Cournot double marginalization pb
Substitutes: do not stifle competition
4
OUTLINE AND TAKE-AWAY POINTS
Static competition
Price-caps can only increase consumer surplus
Coopetition: when do firms agree on price caps?
Mergers vs. price caps
Repeated interaction
Could price caps facilitate undesirable collusion (e.g., by restraining deviations or by facilitating punishments)?
Answer is NO in two environments we were able to study:
• Symmetric firms, stationary equilibrium paths
• Technology adoption model (complete characterization of eq. set)
5
SETTING (1/2)
𝑛 ≥ 2 firms, indexed by 𝑖 ∈ 𝑁 = 1,… , 𝑛
Cost 𝐶𝑖(𝑞𝑖): 𝐶𝑖 0 = 0, 𝐶𝑖′ ∙ ≥ 0
Demand 𝐷𝑖 𝑝𝑖 , 𝑝𝑗
• Downward sloping (𝜕𝑖𝐷𝑖 < 0)
• Uniform price increase reduces demands ( 𝜕𝑗𝐷𝑖𝑗∈𝑁 < 0)
Substitutes or complements
(𝑆) Substitutes: 𝜕𝑗𝐷𝑖 > 0 for 𝑗 ≠ 𝑖
(𝐶) Complements: 𝜕𝑗𝐷𝑖 < 0 for𝑗 ≠ 𝑖
[Hybrid cases as well]
6
SETTING (2/2)
Assumptions
Profit function π𝑖 p = 𝑝𝑖𝐷𝑖 p − 𝐶𝑖(𝐷𝑖 p ) is strictly quasi-concave in 𝑝𝑖
Best-response 𝑅𝑖 p−𝑖 = argmax𝑝𝑖π𝑖 p satisfies 𝜕𝑗𝑅𝑖𝑗≠𝑖 < 1
Occasionally useful to further assume, under 𝑆 :
(𝑆𝐶) Strategic Complements: 𝜕𝑗𝑅𝑖 > 0 for 𝑗 ≠ 𝑖
[often the case under (𝑆)]
Industry profit Π p = π𝑖 p𝑗∈𝑁 is strictly quasi-concave and
achieves its maximum for pM
7
NON-REPEATED INTERACTION: PRELIMINARIES
Lemma
There exists a unique Nash equilibrium
Under (𝑆), all monopoly prices lie above the best-responses
Under (𝐶), at least one monopoly price lies below the best-response
Proposition 1: Price caps
Price-cap implementable prices are those below the best-responses
Intuition: strict quasi-concavity
If 𝑝𝑖 > 𝑅𝑖 𝑝𝑗 , firm 𝑖 lowers its price to its best-response (doable)
Conversely, if p = 𝑝1, 𝑝2 satisfies 𝑝𝑖 ≤ 𝑅𝑖 𝑝𝑗 for 𝑖 = 1,2, then price caps p = p implement p: firms want to raise their prices, but cannot.
8
NON-REPEATED INTERACTION: DUOPOLY (1/3)
Assumption A
For any 𝑗 ≠ 𝑖 ∈ 1,2 and any price 𝑝𝑖 ≤ 𝑝𝑖𝑁, if 𝑅𝑗 𝑝𝑖 > 𝑝𝑗
𝑁 then
𝑅𝑗′ 𝑝𝑖 > −
𝐷𝑖 𝑝𝑖,𝑅𝑗 𝑝𝑖
𝐷𝑗 𝑅𝑗 𝑝𝑖 ,𝑝𝑖
Holds for instance under 𝑆𝐶 (𝑅𝑗′ ⋅ > 0) or when demand is
quasi-symmetric
Proposition 2: Price caps benefit consumers
Any other prices than Nash that can be sustained with price caps yield strictly more consumer surplus than Nash
9
NON-REPEATED INTERACTION: DUOPOLY (2/3)
Intuition
Implementable prices lie below best-responses
At worst on a best-response
Moving from pM toward p:
𝑑𝑆 = − 𝐷1 + 𝐷2𝑅2
′ 𝑑𝑝1 > 0
(+) (−)
Np
Price-cap implementable
prices
0
2R
2p
1p
1R
p
10
NON-REPEATED INTERACTION: DUOPOLY (3/3)
Proposition 3: Will firms use price caps?
Under 𝑆 :
• Price caps cannot increase both firms’ profits (hence, not used in the absence of side payments)
• Under 𝑆𝐶 , cannot even raise industry profit
Under (𝐶), price caps can raise both firms’ profits
Proposition 4: Price caps versus mergers
If 𝑝𝑖𝑀 ≥ 𝑝𝑖
𝑁 for 𝑖 = 1,2, with at least one strict inequality, then a merger harms consumers; price caps can only benefit them.
If 𝑝𝑖𝑀 ≤ 𝑝𝑖
𝑁 for 𝑖 = 1,2, and 𝑝𝑖𝑀 ≤ 𝑅𝑖 𝑝𝑗
𝑀 for 𝑗 ≠ 𝑖 ∈ 1,2 , then a merger and price caps yield the same outcome.
11
NON-REPEATED INTERACTION: SYMMETRIC OLIGOPOLY
Assumptions
Symmetric costs and demands
Reaction curve when others charge same 𝑝 has slope < 1
Results
Proposition 5: Price caps benefit consumers
Proposition 6: Firms’ incentives
• Under 𝑆 , firms cannot gain from price caps
• Under 𝐶 , can sustain monopoly outcome
(uniquely so if non deceasing returns to scale)
12
REPEATED INTERACTION: SYMMETRIC OLIGOPOLY (1/4)
Setting
At date 0, firms agree on price caps.
At date 𝑡 = 1,2,…, firms set prices
Profit: 𝛿𝑡π𝑖 p𝑡𝑡≥1
Assumptions
Symmetric costs and demands
Symmetric, stationary equilibrium paths [no restriction off the equilibrium path.]
If price caps: 𝑝 𝑖 = 𝑝
13
REPEATED INTERACTION: SYMMETRIC OLIGOPOLY (2/4)
Let 𝑃+ (resp., 𝑃𝑐+) denote the set of equilibrium prices p that are
(weakly) more profitable than the static Nash equilibrium and can be sustained in the absence of price caps (resp., with price caps).
Lemma: 𝑝𝑁 ∈ 𝑃+ ⊆ 𝑃𝑐+
Proposition 7: Price caps and tacit coordination
Under 𝑆 and 𝑆𝐶 , price caps have no impact on the scope for tacit coordination
Under 𝐶 , price caps enable perfect coordination, which benefits consumers
(uniquely so if non deceasing returns to scale)
14
REPEATED INTERACTION: SYMMETRIC OLIGOPOLY (3/4)
Intuition: 𝑆 and 𝑆𝐶
Let 𝑝 be sustained by cap 𝑝 ≥ 𝑝
optimal punishment: lowest cont. value 𝑉𝑖
best deviation (on/off-eq): on reaction curve
0 < 𝑅′ ⋅ < 1: price cap never constrains deviations
1p
2R
1R
Np
p̂
p
Mp
0
15
REPEATED INTERACTION: SYMMETRIC OLIGOPOLY (4/4)
Intuition: 𝐶
Suppose 𝑝 = 𝑝𝑀:
If prices ≠ 𝑝𝑀, 𝑝𝑀 in one period, one firm must get less than π 𝑝𝑀, 𝑝𝑀 / 1 − 𝛿
But can guarantee itself π 𝑝𝑀, 𝑝𝑀 / 1 − 𝛿 by playing repeatedly 𝑝𝑀 because 𝐶 and non-decreasing returns to scale
1p
2p
2 (if SC)R
1 (if SC)R
Np
Mp
0
2 (if SS)R
1 (if SS)R
Mp p
Mp p
16
REPEATED INTERACTION: TECHNOLOGY MODEL (1/5)
Setting (special case of Lerner-Tirole AER 2004)
Two symmetric firms 1 and 2 (extension to n > 2, asymmetry)
Users’ value
• 𝑉 − 𝑃 − with both products (patents) at total price 𝑃
• 𝑉 − 𝑒 − 𝑝 − with one product (either one) at price 𝑝
𝑒: essentiality parameter
: adoption cost, distributed according to 𝐹 on [0, 𝑉]
17
REPEATED INTERACTION: TECHNOLOGY MODEL (2/5)
Simple set-up
All users pick the same basket if they adopt the technology
Menus do not increase profit under joint marketing
→ avoids discussing (mixed) bundling & price discrimination
Hybrid demand
From perfect substitutes to perfect complements as 𝑒 increases
• Complements for low prices (users favour full technology)
• Substitutes for high prices (users favour partial technology)
Pool is socially desirable if 𝑒 > 𝑝𝑚 = argmax𝑝 𝑝𝐹 𝑉 − 2𝑝
18
REPEATED INTERACTION: TECHNOLOGY MODEL (3/5)
Repeated interaction without price caps Coordination easiest when lack thereof is very costly Substitutes: collusion involves loss of efficiency/demand
No collusion
or cooperation
1
1
2
0Mp
e
Rivalry Complementors
Perfect cooperation
0V
( )C e
( )C
e
Inefficientcollusion
( )R e
at Mpat Mp
Limited
cooperation
19
REPEATED INTERACTION: TECHNOLOGY MODEL (4/5)
Repeated interaction with price caps No impact of price caps for substitutes Higher consumer surplus and profit for complements
No collusion
1
1
2
0Mp
e
Rivalry Complementors
0V
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Inefficientcollusion
at Mp
Perfect cooperation
at Mp
perfect cooperation and
Price caps enable
lower price to Mp
20
REPEATED INTERACTION: TECHNOLOGY MODEL (5/5)
Does “independent licensing” suffice?
Independent licencing
• Guidelines (US, Europe, Japan,. . . ): Patent pools must allow independent licensing
• Lerner – Tirole 2004: Perfectly screens in good pools and out bad pools in absence of tacit coordination (Boutin 2016)
Price cap = independent licensing + unbundling
With tacit coordination, independent licensing still useful, but no longer a perfect screen
21
CONCLUDING REMARKS (1/3)
When is commercial cooperation is desirable?
(complements vs. substitutes)
Relevant for IP rights, but also in many other industries
content carried by cable operators
payment systems used by merchants
airline alliances and code-sharing agreements
providers included in health insurance networks (Katz 2011)
music performance rights licensed by Pandora
22
CONCLUDING REMARKS (2/3)
Review of mergers and joint marketing agreements (JMAs) plagued by limited information price/demand data patchy or non-existent
evolving patterns of complementarity/substitutability
price-dependent patterns of complementarity/substitutability
→ Calls for information-light rules
Here: price caps as an alternative to mergers and JMAs enable firms to solve Cournot’s problem in case of complements,
but not to raise prices in case of substitutes
if used by firms, raise consumer welfare
• non-repeated interaction
• repeated interactions (in environments studied in this paper)
23
CONCLUDING REMARKS (3/3)
Alleys for future research
Theory of repeated interaction for general cost and demand
Market transparency and focal points
Non-linear pricing and price discrimination
Cooperation on other dimensions
• Cross licensing
• R&D
• Production capacity