Multilateral Negotiations

1
Multilateral Negotiations

• Bargaining with more the two players

2
Coalitional bargaining

• Also called, core bargaining the basis of
  added value
• We may not be able to pin down exactly what will
  happen in a negotiation
• But we can rule out certain outcomes
• That will allow us to figure out the range of
  possible outcomes
• Basic idea
• Individuals and Groups should never get less
  than their outside option ( what the group could
  get if they split off went on their own)

3
Basics of multi-party bargaining

• Each person or sub group should never get less
  than their outside option
• Because they can always split off and go their
  own way
• No individual or subgroup can get more than their
  added value ( the extra surplus their presence
  creates)
• Because all others can always throw you out!

4
The Core with 2 Players

• How does this relate to 2-person bargaining?
• You will never get less than your BATNA,
  otherwise youll give up on negotiations and take
  your BATNA
• Depending on bargaining skill and the other
  factors described, youll get more or less of the
  surplus.
• (If you are evenly matched in skill, delay
  costs, and risks of breakdown, youll get half
  the surplus. But that is less certain than that
  you should never accept less than your BATNA)

5
The Core

• Consider the coalition of all players
• An allocation or competitive distribution just
  refers to a split of the total payoff available
  to all players
• An allocation is blocked if some individual or
  subgroup is better off separating and going their
  own way (i.e. the allocation does not give them
  their outside option)
• An allocation is in the core if it cannot be
  blocked by any individual or coalition

The core is the range of likely bargaining
outcomes
6
Airline JV example

• Three airlines, A, B and C are negotiating a
  joint venture
• By allying themselves, the airlines can offer
  business customers unbroken service from Europe,
  through the US to Asia (and back)
• An airline not joining the JV receives no surplus
  (BATNA 0)
• Airlines A and C create no surplus alone
• A and B can generate 100m without C
• B and C can generate 150m without A
• If all three work together, a 200m surplus is
  generated
• Note
• Airline B is critical to the JV
• This should influence what it gets as a result of
  negotiations

7
Airline example

• What is the range of likely bargaining outcomes?
• Is an equal split likely? No!
• Under an equal split, A, B and C each get 200/3
  ? 66.7.
• B and C get an aggregate payoff of 400/3 ?
  133.3.
• But, B and C can produce 150 on their own
• Rather than take 66.7 each to join the big JV,
  they could form their own JV and get, say, 75
  each!
• Cant imagine B and C would ever freely agree to
  such a deal
• Essentially, A and C compete to obtain Bs
  productive services
• A competitive distribution is one where A and B
  together get at least 100 B and C together get
  at least 150 and the total 200 is divided up
• For example, if B got 150 and neither A nor C
  got anything, the stability requirement would be
  satisfied, but not the feasibility requirement
• On the other hand, B getting the whole surplus of
  200 is competitive
• So is B gets 50, A gets 50 and C gets 100
• There are many other possibilities, some of which
  may be much more likely than others

8
Another example

• Suppose that there are three agents.
• Together they can generate 120 in value.
• Individually they can not generate any value.
• Any coalition of 2 agents can generate 100.
• Conclusion there is no stable allocation the
  core is empty.

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The empty core problem

• What happens where there is an empty core?
• Solutions
• This can be solved if one party seizes the
  initiative and acts first to commit to certain
  aspects of the bargain
• Change in ownership
• Repeated interactions

10
Lessons on multi-party bargaining

• The core sets the range of bargaining outcomes
• No player or sub group gets less than their
  outside alternative
• No player or sub group gets more than their added
  value
• But the core may not exist unstable bargaining
• As before, in some cases a player can seize the
  initiative and set the rules of bargaining to
  favour themselves

11
Added Value

• A useful tool in multilateral bargaining

12
V the total surplus

• The number of possible transactions in a market
  is HUGE
• Under arms-length transactions, freely
  undertaken, there is no reason for agents to
  engage in inefficient deals
• Any group of agents engaged in inefficient deals
  can do better relative to any feasible
  compensation scheme under the inefficient regime
  by switching to an efficient deal and splitting
  up the additional value among themselves
• No agent has a built-in advantage
• No one gets to make take-it-or-leave-it offers
  (agents negotiate until everyone is satisfied)
• No one has an information advantage (relative to
  knowing the available opportunities facing the
  various groups)
• So, think of the entire market as a team whose
  objective is to maximize the aggregate surplus
  (just like we did in the 2-agent case)
• This maximum quantity of economic value is V

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How is V measured?

• Total Surplus
• Economic surplus same idea as 2-agent case

14
Cooperative DM Added Value

• Remember To find the actions that maximise
  surplus, think of the bargaining players as a big
  team or a family, doing whats best for the
  group.
• Added Value roughly, the economic profit from
  you cooperating with the rest of the group
• maximise the pie, cooperate
• (Group
• you) a new option! Others
  cooperate, but
• you dont cooperate with rest of group

no cooperation
15
Your added value

• What is your economic contribution to the market?
• A certain amount of surplus can be produced
  without you
• Denote this amount V-you
• Since V is efficient, V-you must be less than V
• With you, V is possible
• Hence, the amount of value you contribute is V
  V-you
• We call this difference your added value
• Denote this avyou
• Note V-you is the maximum surplus all other
  agents can produce if you refuse to transact with
  them

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What is your Added Value?

• Put simply,

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You cant get more than avyou !

• Why will the other agents never agree to deal in
  which your a payoff surpasses your added value?
• Because, rather than agreeing to a deal in which
  ?you gt avyou, the other agents can
• Tell you to sd-off,
• produce V-you, and
• Share it in such a way that they are all better
  off
• To put it differently, any distribution in which
  ?you gt avyou fails the stability requirement
  because

18
Implication limit their added value!

• A key aspect of modern strategy
• try to limit the added values of other agents
  
• make them dispensable!
• If the other agents added values are small
  relative to yours, you may have the opportunity
  to appropriate a much larger share of the pie
• In fact, if they are sufficiently small, you may
  be guaranteed an economic profit (payoff above
  your BATNA)
• Suppose
• You must get ?you gt BATNAyou! (why?)

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Competitive Advantage

• Can the Added Value framework tell us something
  about what gives a firm a competitive advantage
• What is competitive advantage?

20
Our definition of competitive advantage

• ? Competitive alternatives guarantee
  appropriation above next-best alternative (in the
  context of the firm liquidation value)

Firms Appropriation
Total Surplus
Value tocompetitors
Aggregate End-User Value less Economic
Resource Cost
Appropriation through super-competitive means
(bargaining)
Appropriation guaranteed by competition
Appropriation available from next-best alternative
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Example 1 Pure Bargaining

• Suppose you have one firm, F1, and one buyer, B1.
• The firm can produce 1 unit at zero cost
• The buyer only wants to buy 1 unit with WTP 1
• F1 and B1 both have AVs of 1
• But the most F1 can guarantee itself through
  competition is 0.
• E.g., B1 makes a TIOLI offer to F1

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Example 2 Pure Competition

• Outside options
• B1 can buy product from another for 0.50.
• F1 can liquidate assets for 0.50
• TS WTP WTS 0
• Minimum F1 can guarantee itself is 0.50 which is
  equal to its (new) WTS
• No competitive advantage.

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Example 3 Capacity Constraints

• F1 has one unit of capacity
• B1 and B2 value one unit each at 1
• Outcome
• F1 sells to one buyer
• Can guarantee itself a price of 1 as B1 and B2
  compete with one another
• F1 has a competitive advantage

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Example 4 No capacity constraints

• F1 can produce 2 or more units
• B1 and B2 value one unit each at 1
• Outcome
• F1 sells to both buyers
• Cannot guarantee a profit above 0.
• F1 does not have a competitive advantage

25
Summary

• Competitive advantage means you can appropriate
  surplus even if you are not a good negotiator.
• Need positive AV to appropriate surplus through
  bargaining
• Positive AV is no guarantee of appropriating
  surplus
• Need also to limit the AV of others and create
  competition
• If others AV is limited then have a competitive
  advantage

26
Monopoly

• What is a monopoly and is it bad?

27
What is a monopoly?

• A monopoly is a market with a single producer.
• All of the substitutable products are controlled
  by the same player.

28
Examples

• Trains
• Water service
• Australia Post?
• Large employer in a small town
• Quality monopolies Sony Trinitron, Nintendo
  Entertainment System
• Microsoft

29
Its All in the Cards

• I have 10 red cards
• 10 students each have 1 black card
• A red card and a black card together are worth
  10 (paid by the Dean)
• Who will get what?

30
Its Mostly in the Cards

• We get another chance to play the game
• But I find there are 3 red cards missing
• Pie is smaller by 30
• Is everyone worse off?

31
Application Several Customers

• Assume that there is a monopolist seller and
  three buyers.
• Also assume that there is sufficient capacity to
  cover all three customers.
• Sellers costs are 2 per unit.
• Each buyer has a WTP of 8.

32
Surplus Created

• What is total surplus in this market?

8 - 2 8 - 2 8 - 2
Produce sell
Surplus 3 x 6 18
Seller and buyers
No trade
0
If the seller has capacity to produce 3 (or more)
units, does it capture all of the surplus?
33
Added Value of a Buyer

• What is the Added Value of Buyer 1?

8 - 2 8 - 2 8 - 2
Sell to 1
AV1 18 - 12 6
Seller and buyers
Dont sell to 1
8 - 2 8 - 2
If the seller has capacity to produce 3 (or more)
units, each buyer has an added value of 6?
34
Value Created

• AV of each buyer 6
• AV of monopolist 18
• ? What is the range that the price of goods can
  take, in each transaction?
• The monopolist derives no bargaining power from
  monopoly its like one buyer facing one seller,
  for each unit.
• ? If prices split the difference, the price will
  be 5 and the monopolist will earn 9 3 ? 5 -
  3 ?2

8
2
35
Limited Supply

• Now suppose that the monopolist can only produce
  two units. Cost per unit is still 2.
• What is total value in this market?
• (8 - 2) 2 12
• What is the added value of a buyer?
• (8 - 2) x 2 (8 - 2) x 2 0!
• the Added Value of buyers has fallen drastically
• According to the core, the monopolist may earn
  12 rather than 9.

36
Competition Among Buyers

• Potential competition from buyer 3
• 3 is the excluded buyer (s)he would like to
  replace 1 or 2
• If either 1 or 2 leave the game, the seller can
  still sell to 3
• No buyer is needed to sell a unit each buyer
  has zero added value.
• However, the presence of excluded buyer 3 is very
  valuable to the monopolist she pushes 1 and 2s
  added value to zero, and they earn less.

37
CORE Bargaining

• CORE bargaining players never get more than
  their added value
• ? What do the buyers get if monopolist sells 2
  units to 3 buyers, each with WTP of 8?

• Any one buyer has zero added value if he does
  not buy from the monopolist, another buyer will
• ? get nothing
• ? P ? 8

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How much capacity?

• Usual trade-off is about uncertainty or
  variability in sales
• Underbuild - lose sales
• Overbuild - pay for unused capacity
• Added-value trade-off
• Underbuild - limit customers added value
• Overbuild - every customer is powerful

39
Good vs Bad Monopoly

• Bad monopoly power refers to the practice of
  firms restricting output (or otherwise destroying
  value) in order to diminish buyers added value.
• If a monopolist can capture most of the value
  without destructive strategies, this is bad for
  its buyers, but good for society.
• Name some good and bad monopolies

40
Water and Diamonds

• Nothing is more useful than water but it will
  purchase scarce anything scarce anything can be
  had in exchange for it. A diamond, on the
  contrary, has scarce any value in use but a very
  great quantity of other goods may frequently be
  had in exchange for it.
• Adam Smith, Wealth of Nations, 1776.
• In 1776, diamonds were relatively rare.

41
Why are diamonds so expensive?

• Relative scarcity caused high value
• Created incentives to find new deposits. This
  was done over the next two centuries.
• There is now an abundance of diamonds.
• Why do they cost so much? DeBeers ...

42
The DeBeers Monopoly

• Almost all of the worlds diamonds sold through
  DeBeers distribution system or Central Selling
  Organization (including Russia).
• DeBeers restricts supply invites a selected
  number of dealers. If they try and speculate they
  are not invited back.
• DeBeers manages demand through marketing.
• How much longer will the monopoly persist?

43
Conditions for Monopoly Power

• When can a firm exercise monopoly power?
• Credibly restrict output (DeBeers)
• Reputation for output reductions (Disney)
• Insufficient plant (Nintendo)
• When cant a firm exercise monopoly power?
• Banking, unions

44
Lessons for a monopoly

• A monopoly needs to consider the costs and
  benefits of limiting supply
• Benefits
• Get bigger slice of the pie
• Prestige value
• May gain free publicity
• May encourage customers to buy slower moving
  parts of range

45
Lessons for a monopoly

• A monopoly needs to consider the costs and
  benefits of limiting supply
• Costs
• Reduces total pie
• May effect customer relationship and future sales
• May create general buyer ill will
• Leaves a hole in the market that may encourage
  entry

46
Multiple buyers and sellers

• Three sellers, 1, 2 and 3,
• Capacities one unit only
• Costs shown
• BATNAs 0
• Three buyers, A and B and C,
• Each buyer views sellers products as identical
• But, they have different WTPs
• So, A will pay up to 7 for a unit of product
  from any firm
• Buyers value 1 unit only

47
Surplus-maximising deal

• Figure this out using marginal thinking
• Does it create surplus to produce one unit?
• Arrange value-maximising transaction
• In this case, it is Seller 1 and Buyer B 7
• If so, does it create more surplus to produce a
  second unit?
• Here there are only 3 units otherwise can keep
  going
• Useful approach Graph WTP in descending and WTS
  in ascending order

48
WTP and WTS with many buyers and sellers

• It is surplus-maximising for
• A and B to produce and sell two units to 1 and 2
• 3 and C do not transact

10
B
8
A
S3
6
C
4
S2
2
S1
Quantity
49
Surplus V
1 sells to B surplus 7 2 sells to A surplus
3 V 10
10
B
8
A
3
6
C
4
2
2
1
50
Competitive Distribution (CD)

• How do you find a competitive distribution?
• (Feasibility) Maximise surplus
• (Stability) Ensure that each coalition is given
  sufficient value
• Could use linear programming (through Excel)
• Or rely on market clearing prices

51
Easier to graph and use market-clearing prices

• Prices are market-clearing when they result in
• No excess supply (too many sellers)
• No excess demand (too many buyers)
• In this setup, market-clearing prices generate
  competitive distributions!

52
Market clearing prices ? CD

• At a price of 6,
• distribution of value is

Feasibility Satisfied?1 ?2 ?3 ?A ?B
?C 10
A few stability requirements
Actual payoffs ?
53
Market-clearing prices

• MCP ? CD in this special case
• Sequence of bilateral deals (no market depth
  i.e., suppliers, distributors)
• Homogeneous goods, heterogeneous agents
• Any price between 5 and 6 generates a CD
• At 5 (lowest competitive price)
• Buyers appropriate their highest competitive
  value
• Sellers appropriate their lowest
• At 6 (highest competitive price)
• Buyers appropriate their lowest competitive value
• Sellers appropriate their highest
• Important the maximum surplus an agent can
  appropriate is not always equal to their added
  value
• If other agents have sufficiently attractive
  alternatives to dealing with you, attaining your
  added value may not be possible
• Using market-clearing prices in this setup always
  gives accurate answers regarding the range of
  surplus an agent can attain
• Check to see that at a price above 6 or below
  5, the implied CD is no longer competitive

54
Outcome with multiple buyers and sellers

• Result Competition from the excluded buyer and
  seller limits range of possible prices
• If either buyer pays more than 6, excluded
  seller 3 will jump in with an offer to sell for a
  little less
• ? price will be pushed down below 6
• If any seller gets less than 5, excluded buyer C
  will jump in with an offer to pay a little more
• ? price will be pushed up above 5.
• ? buyers will be paying similar prices (i.e.,
  between 5 6)
• This is different from the result with a
  monopolist
• With a monopolist, buyers can pay different
  prices, based on their WTP
• But with competition, the presence of excluded
  sellers puts a ceiling on prices

55
Perfectly competitive market

• Same setup as before, with a small change to
  buyer C
• This market is perfectly competitive!
• To demonstrate, show that there is one market
  clearing price!
• The resulting CD is unique

56
Graphical analysis
Feasibility Satisfied?1 ?2 ?3 ?A ?B
?C 10
Only one market clearing price!
New Stability requirements
B
9
?B 3
A
?3 0
7
?A 1
3
6 5
?2 2
?1 4
C
?C 0
Actual payoffs ?
4
2
2
1
57
Interesting
Compare added values with CD in perfectly
competitive market
B
9
?B 3
A
?3 0
7
?A 1
3
6 5
?2 2
?1 4
C
?C 0
4
2
2
1
58
Useful fact adding up ? perfect comp.

• Any time the avs add up to V
• The market is perfectly competitive
• In the unique CDV, every agent gets exactly their
  av
• In such situations, agents are full
  appropriators
• Each agent gets exactly what he contributes
• CDV entirely determined by competitive forces
• PCM does not imply zero economic profit!
• It can be that all agents get zero surplus
• But it is not necessarily so
• This property holds for any unstructured,
  multi-party bargaining situation (i.e., of the
  type described in this lecture not just the
  special case of bilateral homogeneous goods most
  recently discussed above)

59
Understanding undergraduate SD

• As more and more buyers and sellers join the
  market, there is less and less gap between the
  WTP of different buyers and the WTS of different
  sellers
• Lining up the buyers according to their WTP
  starts to look like a smooth line, not a
  staircase
• With many buyers sellers, there is almost no
  variation in the possible prices that can be
  negotiated
• If a seller tries to get a higher price, lots of
  sellers willing to sell for less
• If a buyer tries to get a lower price, lots of
  buyers willing to pay more
• ? the law of one price in a big market,
  most transactions take place at very similar
  prices.
• Ex Foreign exchange markets

60
WTP and WTS with 5 buyers and 5 sellers
61
WTP and WTS with many buyers and sellers

• With many buyers sellers, there is almost no
  variation in the possible prices that can be
  negotiated

At a deeper level, the law of one price is
really an implication of perfect competition,
which does not require huge markets to obtain!
62
Summary

• Examining multilateral bargaining requires
  careful quantitative analysis
• Can use some rules (e.g., market clearing) to
  sometimes simplify the problem
• The main interest is in what actions might change
  negotiations