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  Warm 
20 , 0 
0 , 10 
Chill 
0 , 90 
20 , 0 
What is the unique mixedstrategy equilibrium of the above game?
Let p be the probability of "Warm" for Mars,
and q the probability of "Warm" for Venus.
SOLUTION:
Consider the equilibrium strategy for Mars.
First, we must calculate the expected payoff for Venus from each strategy:
Next, we set these equal, since Venus must be
indifferent between her strategies, in equilibrium:
 90(1p) = 10p
 9090p=10p
 90=100p
 p = 9/10
Calculate the same for Venus using the payoffs for Mars:
 20q = 2020q
 20=40q
 q = 1/2
