QUESTION $1$

Player A has a R$1$ Bill and a R$20$ Bill, and Player B has a R$5$ bill and a R$10$ bill. Each player will select a bill from the other player without knowing what bill the other player selected. If the total of the bills selected is odd, player B gets the two bills that were selected, but if the total of the bills is even, player A gets both bills.

a$)$ Develop a payoff table for this game. $($Place the sum of both bills in each cell.$)$

b$)$ What are the best strategies for each player?

c$)$ What is the value of the game?

d$)$ Which player would you like to be$?$

$[20]$