Chapter 11.4, Problem 10E

Player $R$ has a $\text{\$}2$, a $\text{\$}5$,and a $\text{\$}10$ bill. Player $C$ has a $\text{\$}1$, a $\text{\$}5$, and a $\text{\$}10$ bill. Each player selects and shows (simultaneously) one of his or her three bills. If the total value of the two bills shown is even, $R$ wins $C$ ’s bill; if the value is odd, $C$ wins $R$ ’ s bill. (Which player would you rather be?)

(A) Set up the payoff matrix for the game.

(B) Solve the game using the simplex method discussed in this section. (Remove any recessive rows and columns, if present, before you start the simplex method.)