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Unformatted text preview: Ec1052: Introduction to Game Theory Handout 1 Harvard University 12 February 2004 Problem Set 1 Due: Thursday, 19 February (in class). This problems set requires knowledge of von-Neumann Morgenstern decision theory. Challenging problems are marked with one star. Double-starred ques- tions do NOT count towards the grade. They are very hard and simply for the intellectually curious. Problem 1. This problem looks at the sunk cost fallacy . Your room-mate purchases a ticket for the American Repertory Theater for p = 15 Dollars. His utility function u is quasi-linear in money ( m ) and tickets ( t = 1 if he buys a ticket and t = 0 otherwise): 1 u ( m,t ) = m- p + U if he buys a ticket at price p and t = 1 m if he does not buy a ticket and t = 0 (1) He tells you that its a great play and that he would spend even 20 Dollars to see it. On the day of the performance he discovers that he lost the ticket. You tell him to get another ticket and that there are still seats available. However, your friend is all upset and does not want to buy a second ticket. 1(a) You tell him that he is violating expected utility theory and should buy the ticket before its too late! Why can you make such a sweeping statement? 1(b) Your friend explains to you that he has only 40 Dollars left in his pocket (he has no credit cards). Tomorrow, his girl-friend might come to visit him in Cambridge with 50 percent probability. In this case she wants to be invited for dinner which costs 30 Dollars. If she does not get invited she will leave him for sure which causes him a utility loss of 100 (in Dollar terms). Does your friend have a point in not buying the theater ticket? Did he make the correct decision when he bought the first ticket?...
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