There is a city, which looks like chopped isosceles triangle, as shown below. Citizens live  uniformly distributed all over the city.  Two ice-cream vendors, A and B, must independently set up stores in the city. Each citizen buys  from the vendor closest to their location and when equidistant from both vendors they choose by  coin toss. Each vendor’s aim is to maximize the expected number of customers. A choice of  location by the two vendors is a Nash equilibrium if no vendor can do better by deviating  unilaterally. Does this game have a Nash equilibrium? If so, describe it. If not, explain why not

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