Stanford University Department of Management Science and Engineering Optional Problem Session 6 Winter 2010 Friday, February 26, 2010 Practice Problem 6.1 (Pure Strategy Nash Equilibrium) Students are attending a job fair along a 1 mile stretch of road on campus. They are uniformly distributed along this road and after the job fair oﬃcially starts, the section is sealed oﬀ so that no students can enter or leave. The sunny California day is suddenly interrupted by rain. There are a number of umbrella vendors on this road but the price of an umbrella is regulated by the school. We assume that none of the students like walking in the rain so everyone will purchase an umbrella from the nearest vendor. We also assume that there is no sharing, thus each student will buy exactly 1 umbrella. It is permitted for more than one vendor to set up shop at the same location, in which case they evenly split the business. Let N be the number of vendors on this road. (i) Consider the game where
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