Alex and his girlfriend Betty decide independently whether to go to a soccer game or to...

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Alex and his girlfriend Betty decide independently whether to go to a soccer game or to Eason's concert in the evening. Alex likes to do something together with Betty, and vice versa. However, Alex prefers soccer and Betty prefers the concert. To simplify the game, we assume that the total payoff for Alex and for Betty is the sum of the payoffs (in terms of satisfaction) of being at the preferred place, which gives a satisfaction measure of c units, and being together with the partner, giving a measure of d units. We further assume there were no prior communication. Questions: (i) What are the possible outcomes? Identify all Nash equilibria, if any, and briefly explain. [Note: State any assumptions you have made in solutioning this game.] and (ii) What could have happened if there were prior communications between Alex and Betty? Alex and his girlfriend Betty decide independently whether to go to a soccer game or to Eason's concert in the evening. Alex likes to do something together with Betty, and vice versa. However, Alex prefers soccer and Betty prefers the concert. To simplify the game, we assume that the total payoff for Alex and for Betty is the sum of the payoffs (in terms of satisfaction) of being at the preferred place, which gives a satisfaction measure of c units, and being together with the partner, giving a measure of d units. We further assume there were no prior communication. Questions: (i) What are the possible outcomes? Identify all Nash equilibria, if any, and briefly explain. [Note: State any assumptions you have made in solutioning this game.] and (ii) What could have happened if there were prior communications between Alex and Betty?