You and your good friend Larry are supposed to meet for lunch in Champaign, Illinois. You know you have arranged to meet either at a sports bar, Legends (L), or at a pizza place, Papa Del's (PD), but you cannot remember which and you cannot communicate with each other.

You love pizza and prefer Papa Del's. Larry, on the other hand, would rather go to Legends. Nevertheless, you both much prefer to be together rather than apart.

• If both you and your friend each arrive at Legends, your payoff is 9 and your friend's payoff is 15.
• If both you and your friend each arrive at the Papa Del's, your friend's payoff is 8 but your payoff is 16.
• If you go to Legends and your friend goes to Papa Del's, your payoff is 3 and your friend's payoff is 4.
• If you go to Papa Del's and your friend goes to Legend's, your payoff is 4and your friend's payoff is 2.

If it helps, you can think of these payoffs as units of enjoyment or utility you and your friend derive from the outcomes. (As you recall, while firms maximize profits, individuals maximize utility). Assume that this is a single-play, non-repeated game.

1. Construct a payoff matrix with two choices for each player: L (for Legends strategy) and PD (for Papa Del's strategy). Fill the cells with the correct payoffs. Please put yourself on top and your friend on the left side of your payoff matrix.
2. Do you have a dominant strategy? Explain.
3. Does your friend have a dominant strategy? Explain.
4. Of the 4 possible outcomes, identify which one(s), if any, satisfy the conditions of a Nash Equilibrium. Explain your logic.