Game Theory and Business Strategy

Self Test

Finding Mixed Strategy Equilibria

Question 1

Wumpus

Run

Hide

Hunter

Run

60 , 20	0 , 0
0 , 0	20 , 60

Hide

What is the mixed strategy equilibrium of the above game?
Let p be the probability of "Run" for the Wumpus, and q the probability of "Run" for the hunter.

	p=1/4, q=1/4
	p=1/2, q=1/2
	p=1/4, q=3/4
	p=3/4, q=1/4

Question 2

Your accounting department announces that due to an error in its procedures, the numbers in the game from question 1 are wrong, and actually each number should be multiplied by 2. Does this change the equilibrium?

	Yes
	No
	Maybe
	It depends

Question 3

The deities Mars and Venus often do battle to create the weather conditions on Earth. Venus prefers extreme temperatures (especially heat), while Mars prefers temperate conditions. The payoffs (expressed in Points of Wrath) are given below.

Venus

Warm

Chill

Mars

Chill

20 , 0	0 , 10
0 , 90	20 , 0

Warm

What is the unique mixed-strategy equilibrium of the above game?
Let p be the probability of "Warm" for Mars, and q the probability of "Warm" for Venus.

	p=1/10, q=1/2
	p=1/2, q=1/10
	p=1/2, q=1/2
	p=1/10, q=1/10

Question 4

In the above game, who earns more Points of Wrath (on average) in equilibrium, Mars or Venus?

	Mars
	Venus
	Same
	It depends

see solutions

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