We have two players, who are named Harry and Sally. They each start the game with...

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We have two players, who are named Harry and Sally. They each start the game with 1 dollar in front of them. They alternate in saying either "Stop" or "Continue", starting with Harry. When a player says "Continue", 1 dollar is taken from their pile, and 2 dollars are put in the opponent's pile. As soon as any player says "Stop", play is terminated and each player receives the money currently in their pile. Alternatively, play stops when both players reach 100 dollars. Can you predict the equilibrium outcome of this game using game theory? To help analyze this problem, here is a game tree below. As we do in class, try to think of what your opponent would do, and work backwards. Think of yourself as Harry. Ask yourself at each step what Sally would do. (And remember both players are smart and wonder what the other will do.) If you were Harry, what does that mean for what you should do? And the same if you are Sally. Harry Sally Harry Sally Ilarry ally V FELLEL Continue Continue Continue Continue Continue Stop Stop Stop Stop 1 4 Harry: 1 Sally: 1 0 3 2 2 Stop 3 3 Stop 2 5 Harry Sally 98 98 Harry Continue Continue Continue Continue Stop Stop Stop Stop 97 100 Sally 99 99 98 101 100 100 We have two players, who are named Harry and Sally. They each start the game with 1 dollar in front of them. They alternate in saying either "Stop" or "Continue", starting with Harry. When a player says "Continue", 1 dollar is taken from their pile, and 2 dollars are put in the opponent's pile. As soon as any player says "Stop", play is terminated and each player receives the money currently in their pile. Alternatively, play stops when both players reach 100 dollars. Can you predict the equilibrium outcome of this game using game theory? To help analyze this problem, here is a game tree below. As we do in class, try to think of what your opponent would do, and work backwards. Think of yourself as Harry. Ask yourself at each step what Sally would do. (And remember both players are smart and wonder what the other will do.) If you were Harry, what does that mean for what you should do? And the same if you are Sally. Harry Sally Harry Sally Ilarry ally V FELLEL Continue Continue Continue Continue Continue Stop Stop Stop Stop 1 4 Harry: 1 Sally: 1 0 3 2 2 Stop 3 3 Stop 2 5 Harry Sally 98 98 Harry Continue Continue Continue Continue Stop Stop Stop Stop 97 100 Sally 99 99 98 101 100 100

Answer rating: 100% (QA)

This is a sequential game with perfect information which means that both players know all the moves ... View the full answer