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Consider two friends, X and Y, who want to meet at a cafe
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
Expert Solution
a)
The following game represented in normal form
| Y (Player 2) | |||
| X (Player 1) | R | L | |
| R | (2, 1) | (0, 0) | |
| L | (0, 0) | (1, 2) |
When the players arrive at separate cafes, payoff is 0 for both. The player gets the payoff of 2 when their preference is satisfied. When the players meet at cafe different from their preference, they get payoff of 1.
The, nash equilibriums in this case will be (R, R) or (L, L).
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b)
When X is going to let Y know where to meet, then he would obviously choose R. And thus Y will automatically have to come to R irrespective of what he prefers.
The equilibrium will be at (R, R).
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c)
| Y (Player 2) | |||
| X (Player 1) | R | L | |
| R | (2, 1) | (0, 0) | |
| L | (0, 0) | (1, 2) |
In case b) the game equilibrium is at (R, R) with payoff (2, 1).
Sub game equilibriums (R, R) and (L, L).
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