There are three people in this problem. Ann owes money to Bob. She has a choice...
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There are three people in this problem. Ann owes money to Bob. She has a choice of either giving him the money back or not. If she gives him the money, then Claire automatically learns about it. If Bob receives the money, he and his friend Claire simultaneously (they cannot see each other when they make this decision) choose to either meet at the Turan entrance or at the Qabanbay Batyr entrance. If they meet at the same place, they happily go spend the money together and get the utility of 2 each (Ann is just happy for her friends and also gets 2). If Bob and Claire go to different places, then they both get the utility of -2. Ann gets the utility of -1 in this case. If Ann does not give the money to Bob (assume that Ann's payoff is 0 then), then Bob has two options. He can either invite Claire for a walk or not. If he does not invite Claire, then everyone's payoff is 0 (nothing happened). If he invites her, then Claire can either accept (then Bob's and Claire's payoffs are 3 each) or reject (then Bob's and Claire's payoffs are -1 each). 1. Find the extensive form of this game 2. Find the normal form of this game 3. Find all the subgame perfect equilibria 4. Are there other Nash equilibria in this game? There are three people in this problem. Ann owes money to Bob. She has a choice of either giving him the money back or not. If she gives him the money, then Claire automatically learns about it. If Bob receives the money, he and his friend Claire simultaneously (they cannot see each other when they make this decision) choose to either meet at the Turan entrance or at the Qabanbay Batyr entrance. If they meet at the same place, they happily go spend the money together and get the utility of 2 each (Ann is just happy for her friends and also gets 2). If Bob and Claire go to different places, then they both get the utility of -2. Ann gets the utility of -1 in this case. If Ann does not give the money to Bob (assume that Ann's payoff is 0 then), then Bob has two options. He can either invite Claire for a walk or not. If he does not invite Claire, then everyone's payoff is 0 (nothing happened). If he invites her, then Claire can either accept (then Bob's and Claire's payoffs are 3 each) or reject (then Bob's and Claire's payoffs are -1 each). 1. Find the extensive form of this game 2. Find the normal form of this game 3. Find all the subgame perfect equilibria 4. Are there other Nash equilibria in this game?
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