Topic 3: Game Theory

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Topic 3 Game Theory Bargaining

• An introduction to sequential games and the
  importance of credibility and commitment
• Paul Kerin Sam Wylie
• MBS Term 3, 2004

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Game Theory and Bargaining

• PLAN
• (a) Introduction to Noncooperative Game Theory
• Introduction to sequential games
• Application sunk costs
• Sequential Games and commitments
• (b) 2 Person Bargaining Games
• Application hold-up
• Develop understanding as to how value is divided.

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Some History

• The tools of game theory are now common-place
  within economics. They were originally developed
  by John von Neumann and Oscar Morgenstern in
  their 1944 book, The Theory of Games and Economic
  Behavior.
• Thomas Schelling in his 1956 book The Strategy of
  Conflict was the first to apply game theory to
  many contexts in social sciences.
• The theory has developed to a high degree of
  mathematical sophistication. The importance of
  this development was signified by the award of
  the 1994 Nobel Prize to three game theorists
  John Nash, John Harsanyi, and Reinhard Selten.

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Introduction to Sequential Games

• Sequential Choices
• Represented by game trees

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Game Trees

• A game tree has choice nodes (squares) for each
  player, and chance nodes (circles) when Nature
  plays.

Pull ball away
Lucy
Accept
Let Charlie Brown kick
Charlie Brown
Reject
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An Entry Game

• Vacuum cleaner market currently has one incumbent
  (Fastcleaners)
• Potential entrant (Newcleaners). It is deciding
  whether to enter the market or not.
• If enters, Fastcleaners has 2 choices
• Accommodate accept a lower market share
• Price war

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Newcleaners Payoffs
100,000 TR - Entry Cost 150,000 - 50,000
Accommodate
Fastcleaners
Enter
Fight Price War
Newcleaners
-25,000 25,000 - 50,000
Keep Out
0 to Newcleaners
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What should it do?

• Newcleaner needs to forecast Fastcleaners
  response
• How does it do this?
• Put themselves in Fastcleaners shoes
• Work out Fastcleaners payoffs

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Work Backwards
N 100,000 F 150,000
Accommodate
Fastcleaners
Enter
Fight Price War
N-25,000 F 25,000
Newcleaners
Keep Out
N 0 F 300,000
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Reduced Game
N 100,000 F 150,000
Enter
Newcleaners
Keep Out
N 0 F 300,000
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Reduced Game
N 100,000 F 150,000
Enter
Newcleaners
Keep Out
N 0 F 300,000
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Backwards Induction

• The predicted outcome of a sequential game can be
  found by solving the game by backwards induction
  start at the end of the game, and eliminate
  responses that are not best responses
• In the entry game, the solution is found by
  finding Fastcleaners best response to entry. If
  Newcleaners enters, Fastcleaners would rather
  accommodate entry than fight a price war. So
  entry is worthwhile
• Notice that the solution is non-cooperative
  Newcleaners and Fastcleaners are not maximising
  the total pie after entry, its 250,000 (
  100,000 to N 150,000 to F) rather than
  300,000. Newcleaners is increasing its share of
  the pie at Fastcleaners expense

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Games with Nature as a player uncertainty

• Try an example, putting the 2 together Should a
  shop stock extra umbrellas this summer?

10, 5
buy
YOU
Rains often 0.2
-5, -10
dont
Stocks extra umbrellas
YOU
10, 2
Rains less 0.6
-5, - 1
NATURE
SHOP
Drought 0.2
YOU
10, - 5
doesnt
0, ?
- 5, 0
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Making Credible Threatsex controlling rotten
kids
(-1, -1)
Punish
Parent

• Refuse to go

Relent
(2, 0)
Difficult Child
Agree to go
(1, 1)
Usually we write (Payoff for first person who
plays, Payoff for second)
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Credibility

• Problem The parent threatens the child with a
  punishment that is not credible, because it hurts
  both the parent and the child. ? The child will
  refuse to go.
• ? Unless the parent can commit to punish if the
  child refuses to go, (s)he cannot convince the
  child to go.
• Similarly, Lucy cannot commit not to pull away
  the ball ? Charlie Brown should not kick
• What are some of the ways to commit in this case?
• reputation
• delegation

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Example Nuclear Deterrence

• What if the US sets up an automatic nuclear
  response?

(1 to USSR, -1 to USA)
Accommodate
USA
Invade Europe
Fight Nuclear War
USSR
(-100 to USSR, -100 to USA)
Dont invade
(0 to USSR, 0 to USA)
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Example Nuclear Deterrence
(1 to USSR, -1 to USA)
Accommodate
USA
Invade Europe
Fight Nuclear War
USSR
(-100 to USSR, -100 to USA)
Dont invade
(0 to USSR, 0 to USA)

• What if the US sets up an automatic nuclear
  response?
• The option to accommodate disappears
• ? USSR will not invade

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Importance of Commitment

• The difficulty to commit to an action can explain
  why some inefficient outcomes can result.

(-1, 2)
Exploit worker
Manager
Agree to work
Dont exploit worker
(1, 1)
Worker
Dont agree to work
(0, 0)
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Employment Contracts

• This game has a Nash equilibrium outcome, where
  the worker does not agree to work and both
  receive a payoff of 0
• It would be an efficiency improvement if the
  manager could commit not to exploit the worker.
  Without such a commitment device, an inefficient
  equilibrium prevails
• This is similar to the Prisoners Dilemma where
  the problem is that both parties need to find
  some commitment mechanism

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Role of Commitments

• You commit to a future action that you would not
  normally want to take, in order to influence the
  choices of other players (preventing invasion,
  inducing the worker to work,...)
• This is different to providing information to
  other players about what actions youll want to
  take
• if you dont study at all, and dont come to
  class, youll fail information
• if you work hard, but still dont understand at
  all, youll fail commitment to a performance
  standard.

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Commitment Mechanisms(Dixit and Nalebuff,
Thinking Strategically)

• establishing a reputation
• writing an enforceable contract
• cutting off communication
• burning bridges behind you
• leaving the outcome out of your control
• (3rd party arbitration, for example)
• moving in small steps
• developing credibility through teamwork
• employing mandated negotiating agents