In a gambeling game player A and player B both have a $1 and $5 bill. Each player selects one of the bills. Each player selects one of the bills without the other player knowing the bill selected. If the bills do not match, player A wins player B's bill. If the bills match player B wins player A's bill.

a. Develop the game theory for this game. The values should be expressed as the gains or losses of player A.

b. Is there a pure strategy? Why or why not?

c. Determine the optimal stratagies and the value of this game. Does the game favor one player over the other?

d. suppose player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should player A do to improve player A's winnings? Comment on why it is important to follow an optimal game theory strategy?

Please show all work.