Community Answer

a. Let's see whether any player has a dominant strategy or not.  Let's first find out the best strategy for friend. You have two strategies to chooses from, you can either choose movie or baseball. When you choose to play movie, your friend can wither choose to play movie or baseball. If he chooses to play baseball then he will get a payoff of 1 but if he chooses to play movie then he will get a payoff of 3. So the best strategy for your friend is to play movie when you are playing movie. When you choose to play baseball again your friend can wither choose to play movie or baseball. If he chooses to play movie he will get a payoff of 0 but if he chooses to play baseball then he will get a payoff of 2. So the best strategy for your friend is to play baseball when you playing baseball. So as you can see your best friend don't have any dominant strategy, his strategy his changing based on what strategy you're playing.  Now let's find out the best strategy for you. When your friend is choosing to play movie you can wither choose to play movie or baseball. If you choose to play movie you will get a payoff of 2 but it you choose to play baseball then you will get a payoff of 0, so the best strategy for you is to play movie. When your friend is choosing to play baseball again you can either choose to play movie or baseball. If you choose to play movie then you'll get a payoff of 1 but if you choose to play baseball then you'll get a payoff 3. So the best strategy for you is to play baseball. Again as you can see their is no dominant strategy for you also, your best strategy is changing based on what your friend is playing.  So neither the friend nor you have a dominant strategy.      b. Now let's calculate the nash equilibria of this game.   As you can see we have two pure strategy Nash equilibrium here. That when you are choosing to play movie, the best strategy for your friend is to play movie and hence we have underlined 3. When you are choosing to play baseball, the best strategy for your friend is to play baseball and hence we underline 2. When your friend is choosing to play movie, the best strategy for you is to play movie and hence we underline 2. And when your friend is choosing to play baseball the ... See the full answer