SLIDE 1
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Page 1
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Game Theory and Strategic Analysis
11. ✓ Static Games and Nash Equilibrium 12. ✓ Imperfect Competition 13. ✓ Explicit and Implicit Cooperation 14. ➥ Strategic Commitment (a) Sequential games and backward induction. (b) How timing matters: Stackelberg games
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Sequential games and backwards induction
Life must be understood backward, but … it must be lived forward. – Soren Kierkegaard
SLIDE 2 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Page 2
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Pirates puzzle
There are 5 pirates, named A,B,C,D,E. They are intelligent and greedy. They have 100 gold pieces to share. Here are the rules of distribution:
Pirate A proposes distribution of coins amongst the pirates. All pirates vote. If the majority vote against, then Pirate A is thrown to the sharks and Pirate B must propose a coin distribution. And so on. Some details:
- 1. Each time, all remaining pirates vote, including the proposer.
- 2. In case of a tie, a proposal is accepted.
- 3. Assume that each pirate votes in favor of a proposal if and only if it gives a
strictly higher payoff than what he/she gets if the proposal is defeated.
What happens?
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Backward induction solution
Pirate A proposes …
[ 98 , 0 , 1 , 0 , 1 ]
- 2. If 2nd round is reached, Pirates B, C, D, E remain:
Then Pirate B proposes …
[ 99 , 0 , 1 , 0 ]
- 3. If 3rd round is reached, Pirates C, D, E remain:
Then Pirate C proposes …
[ 99 , 0 , 1 ]
- 4. If 4th round is reached, Pirates D and E remain:
Then Pirate D proposes …
[ 100 , 0 ] [ A B C D E ]
SLIDE 3 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Page 3
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An entry deterrance game
Part of Exercise 15.1
The figure below illustrates the following strategic situation involving Sony, which currently has a monopoly in the Discman, and JVC, which may enter the market. JVC Sony Enter ( 5 , -2 )
High
( 6 , 6 )
Low
Sony Stay out ( 12 , 0 )
High
( 8 , 0 )
Low
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Suppose Sony is making plans to build a new plant
Sony JVC Large plant Sony Enter ( 4 , -2 )
High
( 3 , 6 )
Low
Sony Stay out ( 11 , 0 )
High
( 5 , 0 )
Low
JVC Small plant Sony Enter ( 5 , -2 )
High
( 6 , 6 )
Low
Sony Stay out ( 12 , 0 )
High
( 8 , 0 )
Low
SLIDE 4
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Page 4
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Game Theory and Strategic Analysis
11. ✓ Static Games and Nash Equilibrium 12. ✓ Imperfect Competition 13. ✓ Explicit and Implicit Cooperation 14. ➥ Strategic Commitment (a) ✓ Sequential games and backward induction. (b) ➥ How timing matters: Stackelberg games
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Pricing game from Session 12
Firm B Low Med High Low 19 20 18 25 10 33 Firm A Med 24 23 28 31 22 38 High 30 15 40 27 34 42
SLIDE 5
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Page 5
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Suppose that Firm B can commit to its price first
Firm B Firm A
( 24 , 23 )
Low ( 19 , 20 ) Low ( 24 , 23 ) Med
( 30 , 15 )
High
( 28 , 31 ) Firm A
Med ( 18 , 25 ) Low
( 28 , 31 )
Med ( 40 , 27 ) High
( 34 , 42 ) Firm A
High
( 10 , 33 )
Low ( 22 , 38 ) Med ( 34 , 42 ) High
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Summary: What are Stackelberg games?
From these ingredients: two players: 1 and 2 player 1 chooses action A1 and player 2 chooses action A2 We can have three different strategic situations, depending on the timing: Simultaneous moves Sequential game in which player 1 moves first Sequential game in which player 2 moves first Such sequential games are called Stackelberg games. Player who moves first is the leader; other player is the follower.
SLIDE 6
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Page 6
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Summary: What about Stackelberg games?
They let us see how timing and strategic commmitment matter. Who is behaving differently in Stackelberg vs. Nash? Follower? Leader?
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Preemptive investments
Your firm is first to develop the next generation memory chip. You thus will be the first firm to install capacity. What are you thinking?
SLIDE 7 P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Page 7
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Wrap up on strategic commitment
When you have the chance to commit, think about:
- 1. In what way you want to influence the other players’ actions.
- 2. How you can achieve this.
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Review (Tuesday) … Session 16 (Thursday)
No new material will be covered in either session! The review session is optional; Session 16 is mandatory
