Alice and Bob are two broke students (neither one knows the other). In the hopes of...

  

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Alice and Bob are two broke students (neither one knows the other). In the hopes of making a bit of money, they each sign up to participate in a version of the famous economics lab experiment: the ultimatum game. The game works like this: the experimenter puts Alice in Bob in separate rooms and then explains the rules. Alice gets one hundred £1 coins and a sack. She puts as many coins in the sack as she likes and then the experimenter delivers the sack to Bob. Bob can then accept the coins in the sack (in which case Alice keeps the coins that she didn't send, and Bob keeps the coins in the sack), or Bob can reject, in which case it's game over-neither Bob nor Alice gets any money. a. Suppose Bob's utility function is UB = MB when Bob has more money than Alice (i.e. when MB > M₁), and UB = MB - (1/2) (MA - MB) when Bob has less money than Alice. How much money does Alice have to put in the sack to get Bob to accept? b. Now suppose Bob's utility function is UB - MB all the time. How much does Alice have to put in the sack to get Bob to accept? c. What is the moral of this story? Alice and Bob are two broke students (neither one knows the other). In the hopes of making a bit of money, they each sign up to participate in a version of the famous economics lab experiment: the ultimatum game. The game works like this: the experimenter puts Alice in Bob in separate rooms and then explains the rules. Alice gets one hundred £1 coins and a sack. She puts as many coins in the sack as she likes and then the experimenter delivers the sack to Bob. Bob can then accept the coins in the sack (in which case Alice keeps the coins that she didn't send, and Bob keeps the coins in the sack), or Bob can reject, in which case it's game over-neither Bob nor Alice gets any money. a. Suppose Bob's utility function is UB = MB when Bob has more money than Alice (i.e. when MB > M₁), and UB = MB - (1/2) (MA - MB) when Bob has less money than Alice. How much money does Alice have to put in the sack to get Bob to accept? b. Now suppose Bob's utility function is UB - MB all the time. How much does Alice have to put in the sack to get Bob to accept? c. What is the moral of this story?

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