wholesale bargaining 06-11-06
TRANSCRIPT
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Wholesale Bargaining: Models
and Antitrust Implications
Joshua Gans
Melbourne Business SchoolUniversity of Melbourne
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Background Papers
Joint work with Catherine de Fontenay
RAND Journal of Economics, 2005
Review of Network Economics, 2005
IJIO, 2004 Bilateral Bargaining with Externalities
Applications
Concentration Measures and Vertical Market Structure
(JL&Eforthcoming)
Markets for Competitive Advantage (w/ Michael Ryall)
Network Bargaining (Martin Byford)
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Wholesale Markets
Posted prices
Spengler (JPE): double
marginalisation
Salinger (QJE): successive
Cournot oligopoly
Take it or leave it offers
Hart and Tirole (1990)
OBrien and Shaffer (1992)
McAfee and Schwartz (1994) Segal (1999)
Marx and Shaffer (2004)
Bargaining
Inderst and Wey (2003)
OBrien and Shaffer (2004)
Segal and Whinston (2001)
Stole and Zwiebel (1996)
Grossman-Hart-Moore
MacDonald and Ryall (2004)
Brandenberger and Stuart
(2006)
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Antitrust Issues: Traditional Views
How do we analysecompetition between
sellers into a wholesalemarket?
Same as any horizontalmarket
Versus countervailingpower from buyers
How do we analyse vertical
restrictions?
Perfect efficient contracting:vertical practices only
chosen for efficiency
reasons
Versus firms with market
power who can use practices
to extract rents
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New Results
Changes in competition (e.g., concentration) in
upstream markets have a different impact on
final consumers than changes in downstream
markets
Vertical practices can have anti-competitive
effects and result in a redistribution of rents
Can use quantitative bargaining models to
analyse trade-offs
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Outline
1. Our Bargaining Model and Result
2. Treatment of Upstream Competition
3. Analysis of Vertical Integration4. Future Directions
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The Research Goal for Strategy
Environmental
Characteristics:
Consumer demand
Resource availability
Production technology
Bargaining power
Surplus
Generated
Surplus
Division
Payoffs to
owners of
factors ofproduction
Given environmental characteristics, what
are the expected payoffs to factor owners?
That is, what determines appropriability.
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Cooperative Bargaining Theory
The Benefits
Relates environmentalcharacteristics to surplus
division Easy to compute
E.g., Myerson-Shapleyvalue is weighted sum ofcoalitional values
The Problems
Presumption thatcoalitions operate to
maximise surplus Requires observable andverifiable actions
Coalitional externalities
are usually assumedaway If considered, impact on
division only (Myerson)
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Non-Cooperative Bargaining Theory
Benefit: Robustpredictions in thebilateral caseNash bargaining
Rubinstein and Binmore-Rubinstein-Wolinsky
Problem: Bilateral casein isolation cannot dealwith externalities
coalitional formation
D1
U1
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We need a theory that can deal with
this Competitive Externalities
Ds and Us may be competing
firms
Cant negotiate
Bilateral Contracts:
Ds and Us cannot necessarily
observe supply terms of
others
Connectedness does notnecessarily imply surplus
maximisation
D1
UA
D2
UB
while being tractable and intuitive.
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Our Approach
Bilaterality
Assumes that there are no actions that can be
observed beyond a negotiating pair
Potential for inefficient outcomes
Non-cooperative bargaining
Does not presume surplus maximisation
Looks for an equilibrium set of agreements
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Our Results
In a non-cooperative model of a sequence of bilateralnegotiations
There exists a Perfect Bayesian Equilibrium whereby Coalitional surplus is generated by a Nash equilibrium
outcome in pairwise surplus maximisation Division is based on the weighted sum of coalitional
surpluses
We produce a cooperative division of a non-
cooperative surplus Strict generalisation of cooperative bargaining solutions Collapses to known values as externalities are removed
Non-cooperative justification for cooperative outcomes
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Some Notation
Actions
qij is the input quantity
purchased by Di from Uj
tij is the transfer from Di to Uj
(A1) Can only observeactions and transfers you are a
party to (e.g., UB and D2cannot observe q11 ort11)
Primitive Payoffs
Di: (qiA+qiB,q-iA+q-iB)ti1ti2
Uj: t1j + t2j c(q1j+q2j)
Usual concavity assumptionson (.) and c(.)
D1
UA
D2
UB
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Network State
Network
Bilateral links form a graph of
relationships denoted byK
Initial state:K=
(1A,1B,2A,2B) If a pair suffer a breakdown
(e.g., D1 and UA), the new
network is created
New state:K= (1B,2A,2B)
(A2) The network state (K) ispublicly observed
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Possible Contracts
BilateralityAs terms of other pairs are unobserved by at least
one member of a pair, supply terms cannot be
made contingent upon other supply contract terms Network Observability
As the network state is publicly observed supplyterms can be made contingent on the network state
Example:
q11(1A,1B,2A,2B) = 3 and t11(1A,1B,2A,2B) = 2 and
q11(1A, 2A,2B) = 4 and t
11(1A, 2A,2B) = 5 and so on.
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Extensive Form
Fix an order of pairs (in this case 4) Precise order will not matter for equilibrium we focus on
Each pair negotiates in turn Randomly select Di or Uj
That agent, say Di, makes an offer {qij
(K), tij
(K)} for all possibleKincluding Di and Uj.
If Uj accepts, the offer is fixed and move to next pair
If Uj rejects, With probability, 1- , negotiations end and bargaining recommences over the
new networkKij. Otherwise negotiations continue with Uj making an offer to Di.
Binmore-Rubinstein-Wolinsky bilateral game embedded in asequence of interrelated negotiations Examine outcomes as goes to 1.
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Beliefs
Game of incomplete information
Need to impose some structure on out of equilibrium beliefs
Issue in vertical contracting (McAfee and Schwartz; Segal) in that
one party knows what contracts have been signed with others and
offer/acceptance choices may signal those outcomes Simple approach: imposepassive beliefs
Let be the set of equilibrium agreements
When i receives an offer fromj of or
i does not revise its beliefs about any other outcome of the game,
{ ( ), ( )}ij ij ij K
q K t K
( ) ( )ij ij
q K q K ( ) ( )ij ijt K t K
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Equilibrium Outcomes: Actions
Bilateral Efficiency
A set of actions satisfied bilateral efficiency if for all ij in
K,
Suppose that all agents hold passive beliefs. Then, as
approaches 1, in any Perfect Bayesian
equilibrium, each qij(K) is bilaterally efficient (given
K).
1 2 ( ) arg max ( , ( ) ( )) ( ( ))ijij x iA iB iA iB j jq K q q q K q K c q q K + + +
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Equilibrium Outcomes: Actions
Suppose that all agents hold passive beliefs. Then, as approaches 1, in any PerfectBayesian equilibrium, each qij(K) is bilaterally efficient (givenK).
Intuition Negotiation order: 1A,1B,2A,2B and suppose that 1A and 1B have agreed to the equilibrium
actions
If 2A agree to the equilibrium action, 2B negotiate and as this is the last negotiation, it isequivalent to a BRW case so they choose the bilaterally efficient outcome
If 2A agree to something else, D2 will know this but UB wont UB will base offers and acceptances on assumption that 2A have agreed to the equilibrium outcome
(given passive beliefs)
D2 will base offers and acceptances on the actual 2A agreement. Indeed, D2 will be able to offer (andhave accepted) something different to the equilibrium outcome
Given this, will 2A agree to something else? D2 will anticipate the changed outcome in negotiations with UB
Under passive beliefs, UA will not anticipate this changed outcome (so its offers dont change)
D2 will make an offer based on:
By the envelope theorem on q2B , this involves a bilaterally efficient choice ofq2A .
22 2 2 2 1 1 1 2 1 2 2 arg max ( ( ), ) ( ) ( ( ))
A A q A B A A B A A B B Aq q q q q q c q q c q q x + + + +
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Equilibrium Outcomes: Payoffs
Result: As approaches 1, there exists a perfect
Bayesian outcome where agents receive:
This is each agents Myerson-Shapley value over
the bilaterally efficient surplus in each network.
( )( )16 3 (1 ,1 , 2 ,2 ) (1 ,1 , 2 , 2 ) 2 (1 , 2 ) (1 , 2 ) ( , ) 2 ( , )UAv A B A B c A B A B j j c j j iA iB c iA iB = + +
( )( )11 6 3 (1 ,1 , 2 , 2 ) (1 ,1 , 2 ,2 ) 2 (1 , 2 ) (1 , 2 ) ( , ) 2 ( , )Dv A B A B c A B A B j j c j j iA iB c iA iB = + +
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Remarks
Stole and Zwiebel adopt a similar approach in proving theirnon-cooperative game yields a Shapley value Make mistake: do not specify belief structure
Our most general statement shows that the solution concept is
a graph-restricted Myerson value in partition function space. The symmetry in the buyer-seller network case masks some additional
difficulties in the general case
There is some indeterminacy in the complete graph case
The cooperative game solution concept has never been stated before
Nor has it been related to component balance and fair allocation So our proof does cooperative game theory before getting to the steps
before
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Ultimate Solution
1 1 1 ( , ) ( 1) ( 1)! ( , )( 1)( )N
p P
i
T P i T P P PT T
N L p v T L N p N T
=
where:
Nis the set of agents
Pis a partition over the set of agents with cardinalityp
PN is the set of all partitions ofN
L is the initial network (i.e., initial set of bilateral links)
LP is the initial network with links severed between partitions definedbyP.
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Additional Results
(No component externalities) Suppose that primitivepayoffs are independent of actions taken by agentsnot linked the agent Obtain the Myerson value over a bilaterally efficient
surplus.
(No non-pecuniary externalities) Suppose that theprimitive payoffs are independent of the actions theagent cannot observe Obtain the Myerson value.
If agreements are non-binding and subject torenegotiation, the results hold.
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Computability
m buyers
S1 S2
( )
1
0 0
1
0 0 0
( 1)
( , 2)2
( 2)( 1) |
2 1
s i
m x
S
s i
m x h i
m s hm m s m s h
s h i
s
m iv v m s
s m i
m s h
m m s i v s hs h m i m h
= =
+
= = =
= +
+ + + +
( , 2)v m s
( ) |v s h
Bilaterally efficient surplus
with m-s buyers supplied by
both suppliers
Bilaterally efficient surplus ifs
buyers are supplied only by S1
and h are supplied only by S2
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Upstream Competition
Why upstream competition should be
treated differently when there iswholesale bargaining?
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2 x 2 Structure (NI)
UA UB
D1 D2
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Model Structure & Notation
2 upstream & 2 downstream assets each with an associatedmanager (necessary for the asset to be productive); integrationchanges ownership but not need to use manager
Uj can produce input quantities, q1j & q2j toD1 andD2 at cost,
cj(q1j, q2j); quasi-convex
D1 earns (gross) profits of 1(q1A,q1B;q2A,q2B); concave in (q1A,q1B)
and non-increasing in (q2A,q
2B).
Industry profit outcomes:
1 1
2 2
1 2 , 1 1 1 2 2 2 2 2 1 1 1 2 1 2,
( ) max ( , , , ) ( , , , ) ( , ) ( , )A BA B
A B q q A B A B A B A B A A A B B Bq q
D D U U q q q q q q q q c q q c q q +
1 11 , 1 1 1 1 1( ) max ( , ,0,0) ( ,0) ( ,0)
A B A B q q A B A A B B DU U q q c q c q
11 1 1 1( ) max ( , 0,0,0) ( , 0)
A A q A A A DU q c q
11 2 1 1 2 1( , ) max ( ,0,0, ) ( ,0)A A B q A B A A DU D U q q c q
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Upstream Merger
UA UB
D1
D2
D2
UA UB
D1
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Incentives to Merge
Upstream firms jointly gain:
One third of the profits from a UB Monopoly
Intuition: the possibility that a breakdown could
generate this was used by downstream firms as
leverage on the other upstream firm
Downstream firms jointly lose this
Face higher transfers
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Impact on Efficiency
Bilateral negotiations for upstream supply under
upstream competition
Bilateral negotiations for upstream supply under
upstream monopoly
No difference in outcomes so no impact on efficiency
1 1 1 1 2 2 1 2max ( , ; , ) ( , )
Aq A B A B A A Aq q q q c q q
1 1 1 1 2 2 1 2 1 2max ( , ; , ) ( , ) ( , )Aq A B A B A A A B B Bq q q q c q q c q q
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Upstream Competition
Changes to upstream competition have a different
impact to changes in downstream competition
Fragmentation amongst downstream firms drives
impact on consumers, input and output choices. Itconstrains upstream market power.
Extreme: permit upstream mergers when there is no
vertical integration
Leads to additional upstream investment (maybe over-
investment)
May lead to reduced downstream entry
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Vertical Integration
What is the competitive impact of
vertical integration?
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Effect of Integration
UA
UB
D1 D2
UA
UB
D1 D2
UA UB
D1
D2
FI
BI
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WillD1 and UA profit from VI?
( )
11 22
11 26
11 2 26
( )
( )
( ) ( )
UC A B
UC A
B B
D D U U
D D U
D D U D U
+
+
FI
BI
UC UM
( )
1
1 221
1 26
11 26
( )
( )
( ) ( )
UC A B
UC A
A B B
D D U U
D D U
DU U D U
+
+
11 22
11 26
( )
( )
UM A B
UM A
D D U U
D D U
+
( )
11 22
11 26
12 1 26
( )
( )
( ) ( )
UM A B
UM A
A B B
D D U U
D D U
D U U D D U
+
+
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Comparisons
FI versus BI
UC versus UM
As downstream products become more differentiated, strategic VI ismore likely under upstream competition than upstream monopoly
1 2 2 ( ) ( ) B A B D D U D U U
( )1 1 2 23
1 2 1 2
( ) ( )
( ) ( )
B B
UM A B UC A B
D D U D U
D D U U D D U U
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Impact on Efficiency
Bilateral negotiations for upstream supply under NI
Bilateral negotiations for upstream supply under VI
Incentive to raise rivals costs
1 1 1 1 2 2 1 2max ( , ; , ) ( , )
Aq A B A B A A Aq q q q c q q
1 1 1 1 2 2 1 2max ( , ; , ) ( , )
Aq A B A B A A Aq q q q c q q
2 1 1 1 2 2 2 2 2 1 1 1 2max ( , ; , ) ( , ; , ) ( , )Aq A B A B A B A B A A Aq q q q q q q q c q q
+
2 2 2 2 1 1 1 2max ( , ; , ) ( , )
Aq A B A B A A Aq q q q c q q
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VI and Foreclosure
Upstream competition
With homogenous inputs (and some symmetry), VI does not change
efficiency
Upstream monopoly
VI leads to industry profit maximisation (with symmetry and
substitutability);D2 is not supplied any inputs
Under FI,D2 still receives a payoff of:
Technical foreclosure but downstream firm still valuable in
disciplining internal negotiations
( )2
11 212
( ) ( ) ( ) D A B i jv FI D D U U DU =
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An Outsourcing Issue
Outsourcing (make vs buy) decision Typically assumes new function or no sunk assets in the
industry Major outsourcing decisions: typically involve existing
assets that must be divested or scrapped Dilemma If outsource to existing firm, vulnerable to lack of upstream
competition in the future (lack of long-term contracts).
If create new independent supplier, assets divested may not
be worth as much. Examples: GE to Matsushita vs Samsung; Motorola to
BenQ.
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Outsourcing Dilemma
UA
D1
UB
D2
UA-U
B
D1 D2
or ?
Create UA
or sell assets to UB?
Integration implies common ownership of assets
Assume that D1 and D2 do not compete and fixed gain from outsourcing,
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Results
D1 chooses to outsource to UB over an independent firm if
Established outsourcing reducesD1s profits by
But increases total upstream profits (UA and UB) by
Always occurs Choose the option that harmsD2 the most; that is where the rents
are coming from
( )1 1 2 1 212 2 ( ) ( ) j A BD D U D D U U
( )1 1 2 1 26 2 ( ) ( ) j A BD D U D D U U
1 2 1 22 ( ) ( ) j A BD D U D D U U
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Summary
Outsourcing and upstream competition
Standard view: more likely to outsource when upstream
markets are competitive
Here: outsourcing incentives stronger if can preserve orestablish upstream market power
Outsourcing and competitive advantage
Standard view: outsourcing gives comp adv
Here: outsourcing more desirable if harms otherdownstream firms but no comp adv as supply on equal
terms
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Quantitative Evaluation
How can mergers impacting on
vertical market structure beevaluated?
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Wholesale Bargaining
Nfirms indexed by i
Each may operate in an upstream and/or
downstream segment
si: downstream share
i: upstream share
Perfect substitutes (downstream)
Market demand:P(Q)
Costs: upstream (Ci(.)), downstream (ci(.))
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Lerner Index for Vertical Chain
Negotiations between i andj:
( )max ( ) ( ,.) (.) ( ) (.) ( ,.)ijq ij ik i ij i jk j j ijk j kP Q q q c q C P Q q c C q
+ +
( )
( ) ( ) ( ) 0
( ) ( ) 1
ji
ij ij
ji
ij ij
Cc
ik jk q qk
Cc
q q ik jk ki j
P Q P Q q q
P P Q q q s sP P
+ + =
+ = = +
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Vertical HHI
The average Lerner index is:
If there is a preference for internal supply,
2
1
N
ii HHI s
=
1 1 1
1 1( / ) ( / )
N N
i i i ii i i iii i s s q Q HHI s q Q
= =+ = +
1
1max{ , }
N
i i iiVHHI s s
==
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Properties
Ranges between 0 (perfect competition) and 10,000
(downstream monopoly)
Collapses to HHI (Downstream) when all downstream
firms are net buyers of inputs or non-integrated If there is integration then VHHI > HHI
Upstream concentration not relevant
Non-integrated upstream mergers do not change VHHI
Only look upstream if merger involves a net supplier
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Some Examples
Example 1: 4 equal sized upstream firms and 10 equal sized
downstream ones Up HHI = 2500; Down-HHI = 1000 = VHHI
Vertical merger leaves HHIs unchanged (no concern) butraises VHHI to 1150 (potential concern)
Example 2: 8 downstream firms with 10% share and a 9 th with 20%
share
If vertical merger involves large firm then HHI does notchange but VHHI goes from 1300 to 1400 (no concern)despite higher concentration.
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Approach #2: Successive Oligopoly
Firms post unit prices in wholesale market
With linear demand and costs (and homogenousinputs):
Like bilateral bargaining but with additionaldistortions (that can be removed by verticalintegration)
( )2
( min[ , ])( min[ , ])1 1
1 min[ , ]1 1 1 1
max[ , ] ( ) i i i j j ji ii
N N N N s s s
j j j j j j s j j j i
VHHI s s s
= = = =
= + +
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Application: Exxon-Mobil in CaliforniaCompany Upstream (Refining) Market Share
(%)
Downstream (Retailing) Market Share (%)
Chevron 26.4 19.2
Tosco 21.5 17.8
Equilon 16.6 16
Arco 13.8 20.4
Mobil 7 9.7Exxon 7 8.9
Ultramar 5.4 6.8
Paramount 2.3 0
Kern 0 0.3
Koch 0 0.2
Vitol 0 0.2
Tasoro 0 0.2
PetroDiamond 0 0.1
Time 0 0.1
Glencoe 0 0.1
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Concentration Measures
ConcentrationMeasure
Pre-Merger Post-Merger Post-Mergerwith ExxonRefineryDivestiture
Post-Mergerwith ExxonRetailDivestiture
Upstream HHI 1800 1900 1800 1900
Downstream HHI 1600 1800 1800 1600
VHHI Contracting 2100 2400 2400 2100
VHHI Cournot 2200 2500 2700 2100
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Future Directions
Other Vertical Practices
Exclusive dealing
Negotiations over linear prices
Quantitative Analysis
Construct simulation model of bargaining
Empirical tests of vertical market structure
concentration measures and pricing