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Consider two friends, X and Y, who want to meet at a cafe

Economics

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Consider two friends, X and Y, who want to meet at a cafe. They have two local options, R and L. X prefers R while Y prefers L. If they meet at the preferred cafe, the pay-off is 2. If they meet at the other cafe, the pay-off is 1. If they arrive at different cafes and do not meet, the pay-off is 0. a) Consider the game when X and Y pick a cafe without communicat- ing. Represent the game using normal form. What would be the Nash equilibrium(s)? b) Consider now if X was going to let Y know which cafe to meet at. Represent the game using extensive form What would be the rollback equi- librium(s)? c) Represent the game in part (b) using normal form. Use the normal form of the game to explain how subgame perfect equilibriums differ from Nash equilibr