Managerial Economics: Applying the Tools Topic 4, Part 2

1
Managerial Economics Applying the ToolsTopic
4, Part 2

• Putting into practice
• 2-person bargaining
• Multiple-person bargaining
• Paul Kerin Sam Wylie
• MBS Term 3, 2004

2
Bargaining process

• In general, we will assume that bargaining
  proceeds as follows
• The players meet and agree on their actions.
• The players then bargain over transfers
• Ex Banks sharing a 1.2m ATM network.
• Agree to share the network
• A offers to pay 0.4m, B refuses and suggests that
  A pay 0.8 m

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Property 1 Efficiency in Bargaining

• So long as good contracts can be written
• The players meet and agree to take the actions
  that maximise surplus (make the pie as large as
  possible).
• unlike other sequential games, a bargaining game
  will be efficient (surplus maximised no wasted
  surplus).
• The players bargain over payments only
• dividing the pie

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Why should bargaining be efficient?

• If Im A, why wouldnt I make an offer that
  included actions that are advantageous for me?
• Ex Unions bargaining over wages and conditions
  dont unions make demands about work conditions?
• Basic idea
• Unless the action is worth more to me than it
  costs B, Im better off asking for more money
  instead
• If B would be willing to give me a benefit that
  costs him 50, I should be able to get 50
  instead.
• Example of a bad negotiation request
• Builders union for the Sydney Opera House
  requested lifetime free tickets to the Opera for
  the builders and their families.

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In-class bargaining exerciseLawnmower games

• Try to answer these questions in 2 different
  ways
• Converting the problem into buying / selling
  (Answer them all this way, before doing part B)
• Thinking about surplus and BATNAs
• -
  -

Payoff to 2 if dont (BATNA2)
Payoff to 1 if dont (BATNA1)
Payoff to 1 if agree
Payoff to 2 if agree
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BATNA Best Alternative To a Negotiated
Agreement

• Remember, parties reach an agreement if they can
  create surplus together.
• Otherwise, they have to do the best they can on
  their own.
• Total payoff to group, if cooperate
• Group
• ( You Total payoff to group
  if dont cooperate
• the other) your BATNA other
  partys BATNA

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BATNAs and splitting the surplus

• Total surplus
• (Payoff to 1 2 if agree) (BATNA1 BATNA2)
• What you get (your payoff, not your profit)
• Your BATNA a half share of the Total
  Surplus
• ? You could just use this approach to figure out
  what happens, but its a little clunky How do
  I give Ned 50 of surplus?
• ? Here is a method to work out what the payments
  should be (but it only works for 2-person games!)

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How to use BATNAs in 2-person bargaining

• Step 1 Figure out what action the group will
  take if they agree, and what action each party
  will take if they dont agree (and therefore
  cant cooperate)
• Total payoff to group, if cooperate
• (You Total payoff to group
  if dont cooperate
• other) your BATNA other partys
  BATNA
• Step 2 Figure out their BATNAs
• Step 3 Pick one of the players (say, Homer)
  Choose the x variable in your equation what
  he pays to Ned, or the share he pays of the costs

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How to use BATNAs in 2-person bargaining

• Step 4 Graph the money going in and out of each
  players pocket
• Then the split-the-surplus bargaining equation
  is
• This equation is equivalent to saying
• Surplus to 1 Surplus
  to 2
• Step 5 Solve the equation for the value of x.
  Use that to figure out the precise money
  transfers.

Payoff to 2 if dont (BATNA2)
Payoff to 1 if dont (BATNA1)
Payoff to 1 if agree
Payoff to 2 if agree
-

-
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Two Player Transactions

• Buyer-Seller Exchange (Bilateral Monopoly)
• Electricity generator and coal mine
• Actors and sequels
• Firm-specific human capital
• Cost Sharing Arrangements
• Research joint ventures
• Back office functions
• Cleaning services
• Revenue Sharing Arrangements
• Research joint ventures
• Producing complementary products

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Bargaining with 3 or more negotiators

• The problems of multi-party bargaining
• The core and the range of bargaining outcomes
• What happens if there is no core?
• Monopoly

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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)

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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!

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Applying CORE Bargaining to 2-person bargaining

• 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)

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The Core

• Consider the coalition of all players
• An allocation 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
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Example

• Three firms, A, B and C are negotiating a joint
  venture (JV).
• If any firm does not join the JV then it receives
  nothing.
• Firm B is critical to the JV. If firms A and C
  just set up the JV alone then they get nothing.
• Neither A nor C is critical to the JV. If A and B
  work together then they get 220m. Similarly if B
  and C work together then they get 200m
• But if all three work together then they get
  300m in total

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Example

• What is the range of likely bargaining outcomes
  (i.e. the core)?
• Is an equal split blocked? Yes! Under an equal
  split, A, B and C each get 100m. So A and B
  together get 200m. But if A and B leave C out of
  the JV, then they get 220m. So the coalition of
  A and B will block an even split.
• To be in the core we need a split so that each
  player gets a positive payoff A and B together
  get at least 220m B and C together get at least
  200m and the total 300m is divided up.
• e.g. A gets 90m, B gets 160m, C gets 50m.

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Application to in-class case

• Here each town by itself pays 30m
• Any two towns together pay only 40m
• All three together pay 66m
• So to be in the core, an allocation cannot
  involve any town paying more than 30m, or any
  two towns paying more than 40m, but all three
  towns in total pay 66m
• But this cannot hold for any allocation there
  is no core for this bargaining problem!

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Application to in-class case
Say Alendale pays a, Burke pays b and Carlton
pays c. Then a, b and c must be no more
than 30m each ab, ac and bc can each
be no more than 40m abc 66m But this is
impossible! To see this a b lt
40m a c lt 40m b c lt
40m
Add up 2a 2b 2c lt 120 So a b c
lt 60 But this is impossible!
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Application to in-class case

• So the problems with bargaining in the in class
  case were caused because there was no core. In
  such a situation there may be no stable
  bargaining outcome.
• Solutions
• This can be solved if one party seizes the
  initiative and acts first to commit to certain
  aspects of the bargain
• (For example, if town A quickly enters a binding
  agreement with town B before town C can respond)

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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

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SURPLUS AND 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
• maximize the pie, cooperate
• (Group
• you) a new option! Others
  cooperate, but
• you dont cooperate with rest of group

no cooperation
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What is Total Surplus?

• Total Surplus
• (And we assume that when you cooperate, you take
  the action that creates the largest total payoff
  for the group.)

What everyone would get if you cooperated with
the group
What everyone would get if there was no
cooperation
-
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What is your Added Value?

• Your Added Value
• Careful!! Your added value is NOT what you get
  from bargaining
• But the Added Value of each player is a strong
  determinant of what you get.

What everyone would get if you cooperated with
the group
What everyone would get if you didnt cooperate
-
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Property 2 You cant get more than your Added
Value

• Why cant you get more than your Added Value
  ( the surplus created by you joining the
  group)?
• Because if you get more than your Added Value,
  the group would get more by refusing to cooperate
  with you.
• Its as if they think about whether or not to
  gang up on you, and exclude you.

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Monopoly

• If you are indispensable to negotiations, your
  Added Value is the whole surplus
• In 2-person negotiations, each persons Added
  Value is equal to the Total Surplus
• Check that using the definitions
• They cant both get their whole Added Value!
• In multi-person negotiations
• If you are a monopoly (or monopsony), your added
  value equals the whole surplus
• In other words, individuals or subgroups that do
  not include you do not get any payoff.

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Applying CORE Bargaining

• In-class exercise Suppose it costs a monopolist
• 2k to produce his 1st unit
• 3k to produce the 2nd unit (so, 5k to produce 2
  units)
• 5k to produce the 3rd unit (so, 10k to produce
  3 units)
• If there are 3 firms buying from the monopolist
  Alpha, Beta, and Kappa, and their
  Willingness-to-Pay is 8k each, what is the total
  surplus? What is their Added Value?
• What is the possible range of prices they will
  pay?

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Property 3 Equity

• In the example above
• Suppose that the monopolist splits the surplus
  with each buyer.
• What is the outcome, in terms of prices?

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Margins and the Core

• When we calculate the Added Value of Alpha, Beta
  and Kappa, we notice a strange outcome
• Each one is being treated as the 3rd customer
• ? Each one is being treated as the marginal
  customer!
• That is, when the others are deciding whether or
  not to throw that customer out of the
  negotiation, they consider that production costs
  will fall to 5k if hes thrown out
• But this thought process happens to each customer
  in turn!
• ? To build intuition, think about what would
  happen if a customer got more than his Added Value

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Surplus and Added Value

• Remember to start by deciding what the players
  will do they choose the surplus-maximising
  action
• Now think about what action maximises surplus if
  one of the players leaves
• Use that to calculate Added Value
• To build intuition, think about Core Bargaining
  as a kind of trading pit for contracts if you
  are about to sign a contract with a group,
  specifying what everyone gets, people can shout
  out alternative offers of contracts
• if any of those offer are more attractive, you
  change.