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P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & MarketsSession 15 • Strategic Commitment Page 1
1 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
2 Sequential games and backwards induction
Life must be understood backward, but … it must be lived forward.– Soren Kierkegaard
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & MarketsSession 15 • Strategic Commitment Page 2
3 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?
4 Backward induction solution
1. First round:
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 ]
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & MarketsSession 15 • Strategic Commitment Page 3
5 An entry deterrance game Part ofExercise 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 )
Highoutput
( 6 , 6 )
Lowoutput
Sony
Stay out
( 12 , 0 )
Highoutput
( 8 , 0 )
Lowoutput
6 Suppose Sony is making plans to build a new plant
Sony
JVC
Large plant
Sony
Enter
( 4 , -2 )
Highoutput
( 3 , 6 )
Lowoutput
Sony
Stay out
( 11 , 0 )
Highoutput
( 5 , 0 )
Lowoutput
JVC
Small plant
Sony
Enter
( 5 , -2 )
Highoutput
( 6 , 6 )
Lowoutput
Sony
Stay out
( 12 , 0 )
Highoutput
( 8 , 0 )
Lowoutput
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & MarketsSession 15 • Strategic Commitment Page 4
7 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
8 Pricing game from Session 12
Firm BLow Med High
Low19
20
18
25
10
33
Firm A Med24
23
28
31
22
38
High30
15
40
27
34
42
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & MarketsSession 15 • Strategic Commitment Page 5
9 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
10 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.
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & MarketsSession 15 • Strategic Commitment Page 6
11 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?
12 Preemptive investments
Your firm is first to develop the next generation memory chip. You thus willbe the first firm to install capacity. What are you thinking?
P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & MarketsSession 15 • Strategic Commitment Page 7
13 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.
14 Review (Tuesday) … Session 16 (Thursday)
No new material will be covered in either session!
The review session is optional; Session 16 is mandatory
