You have probably had the experience of trying to avoid encountering someone, whom we will call...

 

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You have probably had the experience of trying to avoid encountering someone, whom we will call Rocky. In this instance, Rocky is trying to find you. It is Saturday night and you are choosing which of two possible parties to attend. You like Party 1 better and, if Rocky goes to the other party, you get a payoff 20 at Party 1. If Rocky attends Party 1, however, you are going to be uncomfortable and get a payoff of 5. Similarly, Party 2 gives you a payoff of 15, unless Rocky attends, in which case the payoff is 0. Rocky likes Party 2 better, but he is likes you. He values Party 2 at 10, Party 1 at 5, and your presence at either party that he attends is worth an additional payoff of 10. You and Rocky both know each others strategy space (which party to attend) and payoffs functions. (a) Write down the payoff matrix if this is a one-shot game where you and Rocky simultaneously choose which party to attend. Deter- mine all of the Nash equilibria. What is the probability that you and Rocky attend the same party? What is your expected payoff? (b) Now say that the game is played sequentially. You move first, choosing which party you will attend. Rocky observes this and decides which party to attend. What is the subgame perfect Nash equilibrium to this game? Compare this outcome to (a). What does this tell you about the notion of "first mover advantage"? You have probably had the experience of trying to avoid encountering someone, whom we will call Rocky. In this instance, Rocky is trying to find you. It is Saturday night and you are choosing which of two possible parties to attend. You like Party 1 better and, if Rocky goes to the other party, you get a payoff 20 at Party 1. If Rocky attends Party 1, however, you are going to be uncomfortable and get a payoff of 5. Similarly, Party 2 gives you a payoff of 15, unless Rocky attends, in which case the payoff is 0. Rocky likes Party 2 better, but he is likes you. He values Party 2 at 10, Party 1 at 5, and your presence at either party that he attends is worth an additional payoff of 10. You and Rocky both know each others strategy space (which party to attend) and payoffs functions. (a) Write down the payoff matrix if this is a one-shot game where you and Rocky simultaneously choose which party to attend. Deter- mine all of the Nash equilibria. What is the probability that you and Rocky attend the same party? What is your expected payoff? (b) Now say that the game is played sequentially. You move first, choosing which party you will attend. Rocky observes this and decides which party to attend. What is the subgame perfect Nash equilibrium to this game? Compare this outcome to (a). What does this tell you about the notion of "first mover advantage"?

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