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Game Theory class
5. HOTELLING COMPETITION (16 POINTS) Consumers are uniformly distributed along a boardwalk that is 1 mile long. They all like ice cream the same and dislike walking the same. Prices are regulated and equal for every vendor. The cost of producing ice cream is zero. If more than one vendor is at the same location, they split the business evenly (similarly, if two vendors are at the same distance, the consumer goes to each of them with the same probability). Assume that at the regulated prices the maximum distance that a consumer is willing to walk is 1 mile.
3. (8 points)There exists a maximum distance x that consumers are willing to walk such that a pure strategy Nash Equilibrium with 3 vendors exists. Find it. What happens when the maximum distance is greater than a? HINT: You can use that at least one vendor must locate in the center in such an equilibrium and that the entire market must be served for the maximum z.
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