# ps2 - Ec1052: Introduction to Game Theory Harvard...

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Ec1052: Introduction to Game Theory Handout 3 Harvard University 21 February 2004 Problem Set 2 Due: Saturday, 6 March (Irit’s mail folder on the second ﬂoor of Littauer - up the stairs and to your left). 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. Two lawyers go to an expensive restaurant and decide to split the bill. Model the game as a Prisoner’s dilemma in which each lawyer would prefer to order and pay for herself rather than pay jointly. Problem 2. ** Show that the order of elimination of strictly dominated strategies does not matter for constructing the set S . Problem 3. * Assume a Cournot game with three identical ﬁrms that produce a homogenous product at constant marginal cost c and face linear demand p = 1 - Q . Show that this game has a unique Nash equilibrium in pure strategies but is not solvable by the iterated deletion of dominated strategies (unlike the game with two ﬁrms!). Problem 4. Solve the 2/3 of the average game which we did in the ﬁrst class through the iterated deletion of dominated strategies. 4(a) Assume that rationality is not common knowledge amongst students. In particular assume that all students know that they are rational but that they believe their opponents are choosing a random number between 0 and 100. What is the solution of the game now? 4(b)

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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.

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ps2 - Ec1052: Introduction to Game Theory Harvard...

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