You and your OR professor decide to play a coin game. We each use a quarter (25 cents) and a penny (1 cent). We each pick one secretively and then reveal it to the other. If the coins match, I (your professor) win both coins. If the coins don't match, you win both coins. We play this game repeatedly, each time following the same payoff rules. Develop a game theory model for this game.

(a) What is the optimal strategy for you to play?

(b) What is the optimal strategy for me (the professor) to play?