Two similar live music venues, called Chaos and Katacombes, are to be located in one of four districts, D1, D2, D3, D4. The districts are adjacent to each other in this order sequentially (i.e., located on a straight line). Each district has 100 fans who choose one of these two venues to go to on Saturday nights. Each fan goes to the closer venue, and fans are split 50-50 if they are equally close to both, where distance is measured by the number of districts a fan has to get through to reach the venue. If both venues are in the same district then each gets 200 fans on Saturdays. Each venue chooses a district for its location so as to maximize the number of fans who buy a ticket on Saturday nights. The venues choose their locations simultaneously.

a. Find all the Nash equilibria of this location game between the two venues. (5 pts)

b. Are there any strictly dominated strategies? Is there a strictly dominant strategy? (10 pts)

c. Districts D3 and D4 are only connected by a bridge, which is now permanently closed, but district D4 is connected to D2 by a high-speed train. Thus, D2 is now the central district and the other three districts are considered adjacent to D2 (including district D4) but not to each other. Identify all Nash equilibria of this location game under this new scenario, and find the strictly dominated and strictly dominant strategies