3. (50 points total) Rob and Bob are playing a modified version of a matching pennies game. Since Rob and Bob are Kiwis, living in NZ, they are playing the game with 10 cent pieces. Both Rob and Bob simultaneously place a coin on the table. If the coins match, i.e. both show heads or tails, Rob wins and takes both coins. If the coins doing match, i.e. one heads and the other tails, then Bob takes both coins. Additionally, if anyone plays a tails, then that person must also throw a 10 cent coin into Oranga Lake.

a. (10 points) Create the normal form representation of this game (to simply things, you may consider dollar payoffs for utilities).

b. (20 points) Find ALL Nash Equilibria of this game. Make sure to support your answers via discussion and graphical illustration of the best response correspondence.

c. (5 points) Create a normal form representation of the game above without the requirement to throw the additional coin into the lake and calculate ALL Nash Equilibria.

d. (15 points) Compare the predictions of the two games. More specifically, how does the extra rule of throwing a coin into the lake affect the equilibria (more specifically, likelihood of playing heads)? Is there anything you find surprising about this? Explain why this difference must happen in equilibrium.