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A Mechanism Design Approach to Merger Review
Simon Loertscher Leslie M. Marx
FTC, November 2016
Introduction
Mergers raise competitive concerns if they “encourage one or more firms to raise price, reduce output, diminish innovation, or otherwise harm customers as a result of diminished competitive constraints or incentives.” (HMG)
Review often employs tools based on market shares and diversion ratios
HHI UPP Merger simulation
Loertscher and Marx November 2016 1 / 26
Introduction
Recent review by the DOJ of the proposed merger of two oilfield services firms, Halliburton and Baker Hughes, highlighted challenges:
Multi-product firms offering bundled services: cost synergies, demand complementarities, one-stop shopping preferences Some large, powerful buyers (Shell, ExxonMobil) Low and high WTP buyers (low/high value wells) Buyers seek competing bids
DOJ Complaint focused on effects within individual product markets, but then raised multi-product issues as amplifying competitive concerns
Loertscher and Marx November 2016 2 / 26
Introduction
Recent review by the DOJ of the proposed merger of two oilfield services firms, Halliburton and Baker Hughes, highlighted challenges:
Multi-product firms offering bundled services: cost synergies, demand complementarities, one-stop shopping preferences Some large, powerful buyers (Shell, ExxonMobil) Low and high WTP buyers (low/high value wells) Buyers seek competing bids
DOJ Complaint focused on effects within individual product markets, but then raised multi-product issues as amplifying competitive concerns
Loertscher and Marx November 2016 2 / 26
Table of Contents
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Introduction
Loertscher and Marx November 2016 3 / 26
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Introduction
Loertscher and Marx November 2016 4 / 26
This Paper
Provides a mechanism design based approach that allows analysts to capture:
Purchases made through competitive procurement Multi-product suppliers Demand complementarities One-stop preferences Cost synergies Varying buyer power and WTP
Loertscher and Marx November 2016 5 / 26
Mechanism design based approach
Model the market as a mechanism that determines the allocation and payments
View markets as having a mix of weak and powerful buyers Weak buyers:
Must rely on competition among suppliers to police prices Trade whenever buyer value exceeds production cost
Powerful buyers: “Powerful buyers are often able to negotiate favorable terms with their suppliers.” (HMG) Can negotiate a price below what is required for a supplier simply to outcompete rivals Trade only when the production cost is below the buyer’s optimal reserve price
Loertscher and Marx November 2016 6 / 26
Mechanism design based approach
Market outcome maximizes:
α(expected buyer surplus) + (1 − α)(social surplus)
subject to dominant strategy incentive compatibility and individual rationality
α ∈ [0, 1] measures buyer power
Focus on dominant strategy implementation
Loertscher and Marx November 2016 7 / 26
Mechanism design based approach
Market outcome maximizes:
α(expected buyer surplus) + (1 − α)(social surplus)
subject to dominant strategy incentive compatibility and individual rationality
α ∈ [0, 1] measures buyer power
Focus on dominant strategy implementation
Loertscher and Marx November 2016 7 / 26
Key Findings
Merger of firms producing complements can be good for buyers (even without one-stop preferences)
Merger of firms producing substitutes:
Increases price and reduces quantity and buyer surplus Buyer power:
Mitigates without eliminating effects on price and buyer surplus Exacerbates quantity effects
Buyers with low buyer power and low WTP affected most One-stop preferences amplify merger effects, especially when buyer power is low
Loertscher and Marx November 2016 8 / 26
Literature
Merger analysis based on auction models of procurement Waehrer (1999), Waehrer & Perry (2003), Miller (2014)
Mergers with multi-product suppliers O’Brien & Shaffer (2005)
Buyer power and its role in merger analysis Crawford & Yurukoglu (2012), Gowrisankaran, Nevo, & Town (2015), Collard-Wexler, Gowrisankaran, & Lee (2016)
Role of entry in merger analysis Werden & Froeb (1998)
Coordinated effects Gayle, Marshall, Marx, & Richard (2011), Miller & Weinberg (2016)
Loertscher and Marx November 2016 9 / 26
Plan
Setup with multi-product suppliers
Approach to modeling merger
Illustration of results using an example
Loertscher and Marx November 2016 10 / 26
Setup
1 buyer and 2 products A and B
n sellers partitioned into multi-product sellers, M, sellers of only A, denoted A, and sellers of only B, denoted B
Products are perfect complements for the buyer (zero value for each individually)
Value v for the pair if purchased from different suppliers and v1 ≥ v if from the same supplier (common knowledge)
Loertscher and Marx November 2016 11 / 26
Setup: Seller types
Each seller i independently draws a cost type ci from distribution Gi with support [ci , ci ], with ci > v1 (worst types seller never trade), and density gi
Sellers’ types are their private information
The cost type of a multi-product seller is the cost producing both products, whereas the cost type of a single-product seller is the cost of producing only one product
AMulti-product seller i ∈ M can supply only A at cost γi ci
and only B at cost γiBci
A Bγi , γ < 1 are common knowledge i A BIf γi + γi > 1, then there are cost synergies
For i ∈ A, define γA ≡ 1 and for j ∈ B, define γB ≡ 1i j
Loertscher and Marx November 2016 12 / 26
Setup: Seller types
Each seller i independently draws a cost type ci from distribution Gi with support [ci , ci ], with ci > v1 (worst types seller never trade), and density gi
Sellers’ types are their private information
The cost type of a multi-product seller is the cost producing both products, whereas the cost type of a single-product seller is the cost of producing only one product
AMulti-product seller i ∈ M can supply only A at cost γi ci
and only B at cost γiBci
A Bγi , γ < 1 are common knowledge i A BIf γi + γi > 1, then there are cost synergies
For i ∈ A, define γA ≡ 1 and for j ∈ B, define γB ≡ 1i j
Loertscher and Marx November 2016 12 / 26
Setup: Seller types
Each seller i independently draws a cost type ci from distribution Gi with support [ci , ci ], with ci > v1 (worst types seller never trade), and density gi
Sellers’ types are their private information
The cost type of a multi-product seller is the cost producing both products, whereas the cost type of a single-product seller is the cost of producing only one product
AMulti-product seller i ∈ M can supply only A at cost γi ci
and only B at cost γiBci
A Bγi , γ < 1 are common knowledge i A BIf γi + γi > 1, then there are cost synergies
For i ∈ A, define γA ≡ 1 and for j ∈ B, define γB ≡ 1i j
Loertscher and Marx November 2016 12 / 26
Setup: Seller types
Each seller i independently draws a cost type ci from distribution Gi with support [ci , ci ], with ci > v1 (worst types seller never trade), and density gi
Sellers’ types are their private information
The cost type of a multi-product seller is the cost producing both products, whereas the cost type of a single-product seller is the cost of producing only one product
AMulti-product seller i ∈ M can supply only A at cost γi ci
and only B at cost γiBci
A Bγi , γ < 1 are common knowledge i A BIf γi + γi > 1, then there are cost synergies
For i ∈ A, define γA ≡ 1 and for j ∈ B, define γB ≡ 1i j
Loertscher and Marx November 2016 12 / 26
Setup: Payoffs
Players are risk neutral
A buyer’s payoff is 0 if he does not trade, otherwise value minus payment
A seller’s payoff is 0 if she does not trade, otherwise payment minus cost
Loertscher and Marx November 2016 13 / 26
Optimal mechanism
Expected buyer surplus under allocation rule (qA , qB) and payment rule m is:
n
1 A B A B Ec v qi (c)qi (c) + vqi (c)qj (c)− mi (c)
i∈M i∈M∪A i=1 j∈M∪B
i =j
and similarly for social surplus with costs replacing payments
Loertscher and Marx November 2016 14 / 26
Optimal mechanism
Proposition
Using IC and IR, can write the α-weighted objective as:
Ec
�
i∈M
(
v1 − Γα i (ci ))
qA i (c)q
B i (c)
+
i∈M∪A j∈M∪B
i =j
(v − γA i Γ
α
i (ci )− γB j Γ
α
j
(
cj ))
qA i (c)q
B j (c)J
where
Γα i (c) ≡ c + α Gi (c) gi (c)
is the weighted virtual cost.
Loertscher and Marx November 2016 15 / 26
Optimal mechanism: Allocation
Corollary
In the α-optimal mechanism, quantities traded are determined by the maximum among:
1. 0 → no trade
2. v1 − Γα i (ci ) for i ∈ M → qA i = qB
i = 1
3. v − γA i Γ
α
i (ci )− γB j Γ
α
j (cj ) for i �= j → qA i = qB
j = 1
Loertscher and Marx November 2016 16 / 26
Optimal mechanism: Payments to sellers
In the dominant strategy implementation, payments to sellers are defined by threshold cost types
Payment details
Loertscher and Marx November 2016 17 / 26
Merger of multi-product firms
Merged firm’s cost type is the min of the merging firms’ cost types (assumed regular)
Cost of just A is determined by the lowest A-share of cost for the merging firms (similarly for B)
A A A B B Bγij = min{γi , γj } and γij = min{γi , γj }
Loertscher and Marx November 2016 18 / 26
Illustration: Merger of multi-product firms
3 multi-product firms and 2 single-product firms
Merger of 2 of the multi-product firms
Distribution details
Loertscher and Marx November 2016 19 / 26
Merger effects Powerful, High WTP buyers
Pre-merger firm 1 2 3 4 5 Pre-merger revenue share 27 27 27 9 9 Post-merger revenue share 49 31 10 10
HHI = 2349, HHI′ = 3562, ΔHHI = 1213
Loertscher and Marx November 2016 20 / 26
buyer surplus
quantity
20% one-stop pref
Merger effects High WTP buyers
Higher prices, lower output, and lower buyer surplus
Buyer power mitigates price and surplus effects but exacerbates quantity effects
One-stop preference exacerbates price and surplus effects
%Δ
due
to merger
10
price5
buyer power 0
-5
Loertscher and Marx November 2016 21 / 26
quantity
20% one-stop pref
Merger effects High WTP buyers
Higher prices, lower output, and lower buyer surplus
Buyer power mitigates price and surplus effects but exacerbates quantity effects
One-stop preference exacerbates price and surplus effects
%Δ
due
to merger
10
price5
buyer surplus
buyer power 0
-5
Loertscher and Marx November 2016 21 / 26
20% one-stop pref
Merger effects High WTP buyers
Higher prices, lower output, and lower buyer surplus
Buyer power mitigates price and surplus effects but exacerbates quantity effects
One-stop preference exacerbates price and surplus effects
%Δ
due
to merger
10
5
0
-5
price
buyer surplus
quantitybuyer power
Loertscher and Marx November 2016 21 / 26
Merger effects High WTP buyers
Higher prices, lower output, and lower buyer surplus
Buyer power mitigates price and surplus effects but exacerbates quantity effects
One-stop preference exacerbates price and surplus effects
%Δ
due
to merger
10
5
0
-5
price
buyer surplus
quantitybuyer power
20% one-stop pref
Loertscher and Marx November 2016 21 / 26
Which buyers are harmed by the merger?
Change in price due to merger
high
buyer's willingness
to pay
0.0 0.2 0.4 0.6 0.8 1.0
low
buyer power
Loertscher and Marx November 2016 22 / 26
Which buyers are harmed by the merger?
Change in price due to merger
high
buyer's willingness
to pay
0.0 0.2 0.4 0.6 0.8 1.0
low
buyer power
Loertscher and Marx November 2016 22 / 26
Which buyers are harmed by the merger?
Change in price due to merger
high
buyer's willingness
to pay
0.0 0.2 0.4 0.6 0.8 1.0
low
buyer power
Loertscher and Marx November 2016 22 / 26
Which buyers are harmed by the merger?
buyer's willingness
to pay
-2.5%
0.0 0.2 0.4 0.6 0.8 1.0
Change in buyer surplus due to merger
high
low
buyer power
Loertscher and Marx November 2016 22 / 26
Which buyers are harmed by the merger?
buyer's willingness
to pay
-2.5%
0.0 0.2 0.4 0.6 0.8 1.0
Change in buyer surplus due to merger
high
low
buyer power
Loertscher and Marx November 2016 22 / 26
Which buyers are harmed by the merger?
buyer's willingness
to pay
-2.5%
High BP
High WTP
0.0 0.2 0.4 0.6 0.8 1.0
Change in buyer surplus due to merger
high
low
buyer power
Loertscher and Marx November 2016 22 / 26
entrant profit post merger
Effects of entry High WTP buyers
Entry can offset the price effects of the merger, but should we expect entry?
entrant profit pre merger
buyer power 0.0 0.2 0.4 0.6 0.8 1.0
0.02
0.04
0.06
0.08
0.10
0.12
Loertscher and Marx November 2016 23 / 26
entrant profit post merger
Effects of entry High WTP buyers
Entry can offset the price effects of the merger, but should we expect entry?
entrant profit pre merger
buyer power 0.0 0.2 0.4 0.6 0.8 1.0
0.02
0.04
0.06
0.08
0.10
0.12
fixed cost of entry
Loertscher and Marx November 2016 23 / 26
Effects of entry High WTP buyers
Entry can offset the price effects of the merger, but should we expect entry?
entrant profit pre merger
entrant profit post merger
buyer power 0.0 0.2 0.4 0.6 0.8 1.0
0.02
0.04
0.06
0.08
0.10
0.12
Loertscher and Marx November 2016 23 / 26
Effects of entry High WTP buyers
Entry can offset the price effects of the merger, but should we expect entry?
entrant profit pre merger
entrant profit post merger
buyer power 0.0 0.2 0.4 0.6 0.8 1.0
0.02
0.04
0.06
0.08
0.10
0.12
Loertscher and Marx November 2016 23 / 26
Coordinated effects
Not explicit collusion – so no communication Bilateral rotation scheme
Pre-merger: Not profitable for 1 and 3 (or 2 and 3) Post-merger: Profitable for 1-2 and 3
* = tacit collusion between 1 and 3 or between 1-2 and 3
1.0
0.8
0.6
0.4
0.2
0.0
pre-merger post-merger
1 1 * 2 2 * 3 3* 1-2 1-2* 3 3*
firm
profit
Loertscher and Marx November 2016 24 / 26
Conclusion
Take a mechanism design approach to merger review Provide a merger simulation tool that:
Allows a formalization of buyer power Captures auction-based price formation Addresses multi-product issues
Potentially fruitful avenue for future research
More work to be done ...
Loertscher and Marx November 2016 25 / 26
Thank you
Loertscher and Marx November 2016 26 / 26
Payments to sellers
In the dominant strategy implementation, payments to sellers are defined by threshold cost types
For example, suppose that for a given c, seller i supplies both A and B
As seller i ’s cost increases, holding fixed the other costs, i will either cease supplying completely or switch to supplying either only A or only B
AB,− AB,ALet c and c denote the costs for i such that for i i lower costs seller i supplies both A and B and for higher costs she supplies either nothing or only A, respectively
Other threshold types defined analogously
Loertscher and Marx November 2016 27 / 26
Payments to sellers
In the dominant strategy implementation, payments to sellers are defined by threshold cost types
For example, suppose that for a given c, seller i supplies both A and B
As seller i ’s cost increases, holding fixed the other costs, i will either cease supplying completely or switch to supplying either only A or only B
AB,− AB,ALet c and c denote the costs for i such that for i i lower costs seller i supplies both A and B and for higher costs she supplies either nothing or only A, respectively
Other threshold types defined analogously
Loertscher and Marx November 2016 27 / 26
Payments to sellers
In the dominant strategy implementation, payments to sellers are defined by threshold cost types
For example, suppose that for a given c, seller i supplies both A and B
As seller i ’s cost increases, holding fixed the other costs, i will either cease supplying completely or switch to supplying either only A or only B
AB,− AB,ALet c and c denote the costs for i such that for i i lower costs seller i supplies both A and B and for higher costs she supplies either nothing or only A, respectively
Other threshold types defined analogously
Loertscher and Marx November 2016 27 / 26
Payments to sellers
Threshold payments are defined by the threshold types: a trading seller is paid the worst cost the seller could report and still trade the same quantity plus the payment associated with any lower quantity that would have been supplied under worse types
AB,A A,B B,− AB,AIf c < c < c and ci < c , then i supplies A and i i i i B and is paid
AB,A A A,B AB,A B B,− A,B c + γi (c − c ) + γi (c − c )i i i i i
Proposition
Dominant strategy incentive compatibility holds under threshold payments.
Return
Loertscher and Marx November 2016 28 / 26
Distribution details
Model costs as drawn from the truncated Gamma distribution
Two parameters: s1 (shape) and s2 (scale) with mean s1s2
and variance s1s2 2
s1 = 4 for two-product and s1 = 2.5 for one-product sellers s2 = 1 for all
single-product firm cost type (mean=2.5)
2 4 6 8 10 12 14
0.05
0.10
0.15
0.20
0.25
0.30
Return
Loertscher and Marx November 2016 29 / 26
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