The Mathematics of Mixed
Strategies in Game Theory
12
Online Appendix

12A-2
Part 3
Markets and Prices
2. Imagine twin sisters Matilda and Muriel who are selecting their birthday presents. They can each ask their parents for a book or shoes (and their parents always buy them what they ask for). Suppose that each sister only cares about whether or not she is receiving the same present as the other (as opposed to which present she herself receives). Particularly, Matilda values getting something different from her sister and dislikes when they receive the same thing. Muriel, on the other hand, wants to receive the same thing as her sister and dislikes when they receive different presents. Payoffs are as given in the table below:MurielBookShoesMatildaBook–2 , 22 , Shoes2 , –2–2 , a. What are the pure-strategy Nash equilibria, if any?b. What is the mixed-strategy Nash equilibrium?
–2
2
q
–2
2
)
2
2
p
)
p
2
.