Assume that Nicolas and Orson plan to sell soft drinks on a beach this summer. The beach is 400 meters long and sunbathers are spread evenly across its length. Nicolas and Orson sell the similar soft drinks at the same prices, so customers will walk to the closest vendor. Having the soft drink a distance back to one's beach umbrella incurs transportation costs due to walking to and from the vendor takes time and effort, and the soft drink heats up more (and tastes worse) the further a customer has to walk. Furthermore, the coast guard only permits the vendors to locate in one of the following places on the beach, as indicated by the figure shown below.
a) Where will Orson locate if Nicolas puts a stand at the extreme end of the beach? Does Orson's choice result in a Nash equilibrium?
b) Does a Nash equilibrium exist in which both vendors locate in the center?