Economic game theory

ECO 302 Microeconomic Theory Week 11 Homework

Fall 2017 due on Week 12 class

1. What is a “strategy” in game theory? Provide its definition briefly. 2. What is a “Nash equilibrium”? 3. Find the unique Nash equilibrium in the following game (Prisoner’s Dilemma)

Player 2 Deny Confess

Player 1 Deny -1,-1 -20,0

Confess 0,-20 -5,-5

4. Find two pure-strategy Nash equilibrium in the following game (Battle of Sexes)

Wife Soccer Opera

Husband Soccer 2,1 0,0 Opera 0,0 1,2

5. Show that there does not exist a pure-strategy Nash equilibrium in the following game (Matching pennies)

Player 2 Head Tail

Player 1 Head 1,-1 -1,1 Tail -1,1 1,-1

6. In the game given in 5, show that it is a mixed-strategy equilibrium that both players play each action with probability 1/2. 7. What is a “subgame perfect Nash equilibrium”? Provide its definition briefly.

8. Find a subgame perfect Nash equilibrium of the following extensive-form game.

9. Find a subgame perfect Nash equilibrium of the following extensive-form game.