wholesale bargaining 06-11-06

8/14/2019 Wholesale Bargaining 06-11-06

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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 ( , ; , ) ( , )


1 1 1 1 2 2 1 2max ( , ; , ) ( , )


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 ( , ; , ) ( , )



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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

wholesale bargaining 06-11-06

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