Zach and Whitney get really bored while studying for an exam and decide to play a simple game. Here's how it works: each of them holds a penny and chooses, simultaneously, whether to show the head or the tail of their penny. If they show the same side, Whitney wins Zach's penny. If they show different sides, Zach wins the Whitney's penny.
a. Write the payoff matrix for this game.
b. What are the pure strategy Nash equilibria for this game?
c. What is the mixed strategy equilibrium for this game?