Chapter 11, Problem 29RE

Finger game Consider the following finger game between Ron (rows) and Cathy (columns): Each points either $1$ or $2$ fingers at the other. If they match, Ron pays Cathy $\text{\$}2$. If Ron points $1$ finger and Cathy points $2$, Cathy pays Ron $\text{\$}3$. If Ron points $2$ fingers and Cathy points $1$, Cathy pays Ron $\text{\$}1$.

(A) Set up a payoff matrix for this game.

(B) Use formulas from Section 11.2 to find the optimal strategies for Ron and for Cathy.