Problem Set 13 PDF

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Prof. Dr. Sebastian J. Goerg Prof. Dr. Michael Kurschilgen

Economics I Tutorial

Problem Set 13 Question 1 (Nash equilibria) Check for dominated strategies in the following strategic games. Then find the Nash equilibria. a) Opera Football

Opera 3, 2 0, 0

Football 0, 0 2, 3

b) Swerve Straight

Swerve Straight 0, 0 -1, 1 1, -1 -10, -10

Party Home

Party 10, 10 0, 0

Home 0, 0 5, 5

d) Heads Tails

Heads 1, -1 -1, 1

Tails -1, 1 1, -1

c)

e)

Silent Betray

f) Stag Hare

Silent -1, -1 0, -3 Stag 2, 2 1, 0

Betray -3, 0 -2, -2

Hare 0, 1 1, 1

Question 2 (Game with several strategies) A football player and the opposing goal keeper face each other in a championship deciding penalty in the 90th minute of the final game. The player has the alternatives to shoot to the left, into the center or to the right, while the goalkeeper has the same alternatives regarding his actions to save the ball. Given that the player is known to never miss the goal, choose reasonable payouts for both players and illustrate the described game in normal form. What are the Nash equilibria (in pure strategies)?

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