Wholesale Bargaining: Models and Antitrust Implications

1
Wholesale Bargaining Models and Antitrust
Implications

• Joshua Gans
• Melbourne Business School
• University of Melbourne

2
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 (JLE forthcoming)
• Markets for Competitive Advantage (w/ Michael
  Ryall)
• Network Bargaining (Martin Byford)

3
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)

4
Antitrust Issues Traditional Views

• How do we analyse competition between sellers
  into a wholesale market?
• Same as any horizontal market
• Versus countervailing power 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

5
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

• Our Bargaining Model and Result
• Treatment of Upstream Competition
• Analysis of Vertical Integration
• Future Directions

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Cooperative Bargaining Theory

• The Benefits
• Relates environmental characteristics to surplus
  division
• Easy to compute
• E.g., Myerson-Shapley value is weighted sum of
  coalitional values

• The Problems
• Presumption that coalitions operate to maximise
  surplus
• Requires observable and verifiable actions
• Coalitional externalities are usually assumed
  away
• If considered, impact on division only (Myerson)

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Non-Cooperative Bargaining Theory

• Benefit Robust predictions in the bilateral case
• Nash bargaining
• Rubinstein and Binmore-Rubinstein-Wolinsky
• Problem Bilateral case in isolation cannot deal
  with
• 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 not necessarily imply surplus
  maximisation

D1
D2
UA
UB
while being tractable and intuitive.
10
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
  bilateral negotiations
• 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 observe actions and transfers you
  are a party to (e.g., UB and D2 cannot observe
  q11 or t11)
• Primitive Payoffs
• Di p(qiAqiB, q-iAq-iB)ti1ti2
• Uj t1j t2j c(q1jq2j)
• Usual concavity assumptions on p(.) and c(.)

D1
D2
UA
UB
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Network State

• Network
• Bilateral links form a graph of relationships
  denoted by K
• 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) is publicly observed

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Possible Contracts

• Bilaterality
• As 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 supply
  terms 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 t11(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 possible K including Di and Uj.
• If Uj accepts, the offer is fixed and move to
  next pair
• If Uj rejects,
• With probability, 1-s, negotiations end and
  bargaining recommences over the new network K
  ij.
• Otherwise negotiations continue with Uj making an
  offer to Di.
• Binmore-Rubinstein-Wolinsky bilateral game
  embedded in a sequence of interrelated
  negotiations
• Examine outcomes as s 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 impose passive beliefs
• Let be the set of
  equilibrium agreements
• When i receives an offer from j of
  or
• i does not revise its beliefs about any other
  outcome of the game

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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 s approaches 1, in any Perfect Bayesian
  equilibrium, each qij(K) is bilaterally efficient
  (given K).

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Equilibrium Outcomes Actions

• Suppose that all agents hold passive beliefs.
  Then, as s approaches 1, in any Perfect Bayesian
  equilibrium, each qij(K) is bilaterally efficient
  (given K).
• 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
  is equivalent 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
  (and have 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 of q2A.

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Equilibrium Outcomes Payoffs

• Result As s 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.

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Remarks

• Stole and Zwiebel adopt a similar approach in
  proving their non-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

• where
• N is the set of agents
• P is a partition over the set of agents with
  cardinality p
• PN is the set of all partitions of N
• L is the initial network (i.e., initial set of
  bilateral links)
• LP is the initial network with links severed
  between partitions defined by P.

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Additional Results

• (No component externalities) Suppose that
  primitive payoffs are independent of actions
  taken by agents not linked the agent
• Obtain the Myerson value over a bilaterally
  efficient surplus.
• (No non-pecuniary externalities) Suppose that the
  primitive payoffs are independent of the actions
  the agent cannot observe
• Obtain the Myerson value.
• If agreements are non-binding and subject to
  renegotiation, the results hold.

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Computability
m buyers
Bilaterally efficient surplus with m-s buyers
supplied by both suppliers
S1
S2
Bilaterally efficient surplus if s 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 is wholesale bargaining?

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2 x 2 Structure (NI)
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Model Structure Notation

• 2 upstream 2 downstream assets each with an
  associated manager (necessary for the asset to be
  productive) integration changes ownership but
  not need to use manager at same level
• Uj can produce input quantities, q1j q2j to D1
  and D2 at cost, cj(q1j, q2j) quasi-convex
• D1 earns (gross) profits of p1(q1A,q1Bq2A,q2B)
  concave in (q1A,q1B) and non-increasing in
  (q2A,q2B).
• Industry profit outcomes

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Upstream Merger
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Upstream Merger
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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

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Illustrative Example (Distribution)
Merger means that if negotiations breaks down
with one downstream firm, they split monopoly
profits with remaining one.

• Assumptions
• Demand P 1 (q1 q2)
• Costs none
• Symmetry
• Monopoly profits ¼

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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

32
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. It
  constrains 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
BI
FI
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Will D1 and UA profit from VI?
UC
UM
FI
BI
36
Comparisons

• FI versus BI
• UC versus UM
• As downstream products become more
  differentiated, strategic VI is more likely under
  upstream competition than upstream monopoly

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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

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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

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Quantitative Evaluation

• How can mergers impacting on vertical market
  structure be evaluated?

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Wholesale Bargaining

• N firms indexed by i
• Each may operate in an upstream and/or downstream
  segment
• si downstream share
• si 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 and j

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Vertical HHI

• The average Lerner index is
• If there is a preference for internal supply,

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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 gt 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) but raises VHHI to 1150 (potential
  concern)
• Example 2
• 8 downstream firms with 10 share and a 9th with
  20 share
• If vertical merger involves large firm then HHI
  does not change 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 homogenous
  inputs)
• Like bilateral bargaining but with additional
  distortions (that can be removed by vertical
  integration)

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Application Exxon-Mobil in California
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Concentration Measures
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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