Roger and Michelle like going out and enjoy each others’ company, but have different taste in entertainment. Michelle would like to go to a professional basketball game, while Roger prefers opera. If they fail to agree to go together to either the game or to the opera this Saturday night they will stay at home and be miserable. Both will be worse off than if they had gone together to either the game or the opera. (a) Construct a pay-off matrix for this game. (You can make up your own numbers for this problem; just make sure the numbers correctly depict the given situation.) (b) Find two Nash equilibria for this game. Explain why they are indeed Nash equilibria.

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