Please provide a clear step by step solution with graphs, tables etc...

You and a good friend are supposed to meet in Paris, France. You know you have arranged to meet at either the Arc de Triomphe (AdT) or at the base of the Eiffel Tower (ET) but you cannot remember which and you cannot communicate with each other.

You prefer the Arc de Triomphe. Your friend prefers the Eiffel Tower. But you both much prefer to be together rather than apart.

• If you and your friend each arrive at the Arc de Triomphe, your payoff is 12 and your friend's payoff is 8.
• If you and your friend each arrive at the Eiffel Tower, you friend's payoff is 12 but your payoff is 8.
• If you go to the Arc de Triomphe and your friend goes to the Eiffel Tower, your payoff is 5 and your friend's payoff is 5
• If you go to the Eiffel Tower and your friend goes to the Arc de Triomphe, your payoff is 3 and your friend's payoff is 3.

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: ET (for Eiffel Tower strategy) and AdT (for Arc de Triomphe) strategy. Fill the cells with the correct payoffs. Please put yourself on top and your friend on the left side of your payoff matrix.

1. Do you have a dominant strategy? Explain.

1. Does your friend have a dominant strategy? Explain.

1. Of the 4 possible outcomes, identify which one(s), if any, satisfy the conditions of a Nash Equilibrium. Explain your logic.