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Unformatted text preview: Ec1052: Introduction to Game Theory Handout 12 Harvard University 18 April 2004 Problem Set 5 Due: Thursday, 29 April (in class). Challenging problems are marked with one star. Double-starred questions do NOT count towards the grade. They are very hard and simply for the intellec- tually curious. Remember that you can work in groups but you have to write up your own solutions. Good luck! Problem 1. The trust game is a two player game with three periods. Player 1 starts off with 10 Dollars. She can send an amount 0 x 10 to player 2. The experimenter triples the sent amount such that player 2 receives 3 x . Player 2 can then send an amount 0 y 3 x to player 1. 1(a) Draw a diagram of the extensive form of this game. 1(b) Find all the SPE in the trust game. 1(c) Why is this game used to measure trust and trustworthiness? Do you think it provides reasonable measures? How would you interpret reciprocity in this game? How would you detect it? 1(d) ** What is trust? Come up with a operational definition. Problem 2. Compute the set of feasible and strictly individually rational payoffs in the Battle of the Sexes stage game which we did in class (where coordinating on the preferred strategy gives me payoff 3 and the other player payoff 1). Using the folk theorem find the set of normalized equilibrium payoffs which can be implemented through some SPE. Show that for each there is a pure strategy SPE such that the equilibrium payoff of each player in this SPE converges to 3 2 as 1. 1 Problem 3. Two firms produce differentiated output at marginal cost c and they face a demand curve q i = a- bp i + dp j ( b > d ). The owners of both firms care about profit maximization, and hire a manager at time t...
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This note was uploaded on 05/19/2010 for the course DFDAS 220 taught by Professor Ding during the Fall '10 term at Academy of Art University.
- Fall '10