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Unformatted text preview: Ec1052: Introduction to Game Theory Handout 5 Harvard University 6 March 2004 Problem Set 3 Due: Friday, 19 March 2004 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. When I give an exam, my utility is decreasing in the effort it takes me to make up new questions and increasing in the amount of time which students spend learning the material the course covers. I have two options: make up new questions or reuse questions from old exams. In preparing for the exam students also have two choices: to spend their time available for studying trying to learn the course material, or to try to find out what questions were asked in past years and memorize the answers. While I dont necessarily have these sentiments in real life, assume for the purposes of this question that having students only memorize old questions is sufficiently annoying to me that I derive utility from having them fail an exam containing new questions if this is all theyve done. Assume that students care mostly about their score on the exam (but perhaps also about learning) so that if I ask new questions students are best off learning the material, while if I ask old questions they are best off memorizing old answers. Write down what you would think are reasonable utility functions for a typical student and for me (consistent with the description of the game above). Find the Nash equilibrium of the game and comment on how the probability with which I put old questions on the exam is affected by the parameters of the utility function. Problem 2. Find all the Nash equilibria of the following two games....
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