Game Theory and Strategic Analysis 11. Static Games and Nash - - PowerPoint PPT Presentation

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

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 1

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 & Markets Session 15 • Strategic Commitment Slide 2

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?

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 3

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 & Markets Session 15 • Strategic Commitment Slide 4

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

• utput

( 6 , 6 )

Low

• utput

Sony Stay out ( 12 , 0 )

High

• utput

( 8 , 0 )

Low

• utput

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 5

Suppose Sony is making plans to build a new plant

Sony JVC Large plant Sony Enter ( 4 , -2 )

High

• utput

( 3 , 6 )

Low

• utput

Sony Stay out ( 11 , 0 )

High

• utput

( 5 , 0 )

Low

• utput

JVC Small plant Sony Enter ( 5 , -2 )

High

• utput

( 6 , 6 )

Low

• utput

Sony Stay out ( 12 , 0 )

High

• utput

( 8 , 0 )

Low

• utput

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 6

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

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 7

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

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 8

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

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 9

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 & Markets Session 15 • Strategic Commitment Slide 10

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?

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 11

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?

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 12

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.

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 13

Review (Tuesday) … Session 16 (Thursday)

No new material will be covered in either session! The review session is optional; Session 16 is mandatory

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets Session 15 • Strategic Commitment Slide 14