Game Theory

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Game Theory

• Steven Allen
• ECG 507
• Fall 2005

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1. Oligopoly

• Management Challenges
• Strategic actions
• Rival behavior

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2. Oligopoly

• Equilibrium in an Oligopolistic Market
• In perfect competition and monopoly the producers
  did not have to consider a rivals response when
  choosing output and price.
• In oligopoly the producers must consider the
  response of competitors when choosing output and
  price.

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3. Oligopoly

• Equilibrium in an Oligopolistic Market
• Defining Equilibrium
• Firms doing the best they can and have no
  incentive to change their output or price
• All firms assume competitors are taking rival
  decisions into account.
• Nash Equilibrium
• Each firm is doing the best it can given what its
  competitors are doing.

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4. Cartels

• Characteristics
• 1) Explicit agreements to set output and
  price
• 2) May not include all firms
• 3) Most often international

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5. Cartels

• Conditions for success
• Potential of monopoly power--inelastic demand
• Ability to prevent cheating

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6. Cartels

• OPEC Observations
• TD and DOPEC is inelastic
• Non-OPEC supply is inelastic

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7. Payoff Matrix for Cover Game
Newsweek
Harry Potter
Alito
Harry Potter
Time
Alito
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8. Payoff Matrix for Cover Game
Newsweek
Harry Potter
Alito
Harry Potter
35, 35
70, 30
Time
Alito
15, 15
30, 70
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9. Dominant strategy

• Strategy that is optimal no matter what other
  player does
• Examples
• Time, Newsweek both go with Harry Potter
• Send base runners with full count and 2 out

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10. Payoff Matrix for Cover Game
Newsweek
Harry Potter
Alito
Harry Potter
42, 28
70, 30
Time
Alito
18, 12
30, 70
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11. Dominated strategies
Toyota
Large
Small
Dont build
Honda
Large
Small
Dont build
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12. Payoff Matrix for Airline Pricing Game
United
100
200
100
81, 81
123, 58
American
200
112, 112
58, 123
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13. Competition Versus Collusion

• These two firms are playing a noncooperative
  game.
• Each firm independently does the best it can
  taking its competitor into account.
• An example in game theory, called the Prisoners
  Dilemma, illustrates the problem oligopolistic
  firms face.

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14. The Prisoners Dilemma

• Scenario
• KGB accuses Popov and Chekhov of being American
  spies
• They are in separate jail cells and cannot
  communicate.
• Each has been asked to confess to the crime.
• A payoff matrix results from their decision.

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15. Payoff Matrix forPrisoners Dilemma
Chekhov
Rat out Popov
Clam up
Clam up
-2, -2
-25, -1
Popov
Rat out Chevhov
-20, -20
-1, -25
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16. Repeated Games

• In real life, firms play a repeated game.
• With each repetition of the Prisoners Dilemma,
  firms can develop reputations about their
  behavior and study the behavior of their
  competitors.

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17. Strategies for repeated games

• Match or beat prices of competitors
• Sends signal to competitors
• Enforceable as long as costs comparable
• Tit-for-tat
• Simple to execute
• Successful in experiments
• Does not always work in real life (Serbs v.
  Albanians)

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18. Modified tit-for-tat

• Allows for changing conditions, miscommunication
• Four steps
• 1. Begin cooperating
• 2. Continue cooperating
• 3. Track cheating by other side
• 4. Retaliate when cheating has passed acceptable
  level

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19. Charlie Brown v. Lucy Van Pelt
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20. Charlie v. Lucy sequential game
Fall
-10, 10
Kick
Lucy
Kick
10, 0
Charlie
Abort
0, -10
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21. US v. Japan in HDTV
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22. Strategic move by US go first
1, 1
High
High
Japan
Low
3, 2
US
High
2, 4
Low
Japan
Low
4, 3
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23. NATO v. USSR
Conv
1, -1
Attack NATO
US
Nuke
-100,-100
USSR
Status quo
0, 0
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24. An effective response rule
Attack NATO
US
Nuke
-100,-100
USSR
Status quo
0, 0
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25. How to make threats/promises credible?

• Develop a reputation and use it
• Burn your bridges behind you