Gym X and Bodyworks Are Both Going to Open an Exercise

Essay

Gym X and Bodyworks are both going to open an exercise facility in the local market. Each company may decide to open a facility concentrating on cardio equipment for customers interested in mostly aerobic workouts. Another alternative for each company is to open a facility concentrating on muscle building equipment for customers interested mostly in bodybuilding workouts. The payoff matrix for each company dependent upon their strategies and that of their competitor is given below. Does either player have a dominant strategy? Does the game have any Nash equilibria? What is the maximin strategy of each player in the game?