1. Yoda and Skywalker are roommates. They are deciding on who to wash the dishes as neither love to wash the dishes. They come up with a plan where if they collude with each other, the dishes get done by an outsider who they can pay for their services and they are better off significantly. However, if they fight, they are worse off. Hence, they have 2 possible strategies- either cooperate or fight. If both players cooperate, they get a payoff of 200 and if they fight, they gain a payoff of -50. If one player cooperates, the one who cooperates gets a payoff of -100 and the one who fights gets a payoff of 350.

• Write the payoff matrix of this game
• Suppose now the payoffs for one player cooperating and the other fighting is the same and is equal to 70 what is the Nash equilibrium for this game.
• Suppose the payoff for both fighting is now 0, using information from the previous question, what is the Nash equilibrium for this game.
• Are there any dominant strategies in this game?