Question: You operate a fitness center, Durim, in the center of Tirana, (the capitol of Albania). Your only rival in the area is a fitness center called Palester. Your two firms form a duopoly (oligopoly with 2 firms) over Tirana's gymnasium market. You and the manager of Palester use game theory to make important decisions. For each of the following decisions, identify all the Nash Equilibria. Identify the "socially optimal" equilibria as well (the one that maximizes the sum of both player's payouts).
1. Advertising. Durim and Palester much choose how intensely to advertise (high or low). If both choose high, each firm will increase profits by $200. If both choose low, each firm will increase profits by $100. If one firm chooses high while the other firm chooses low, the high-intensity firm will earn $500 in extra profits while the low-intensity firm will lose $100 in profits.
2. Expansion. Durim and Palester much choose whether or not to expand their facilities. Expansion comes at a cost of $1000. If both firms expand, revenues for each firm will increase by $800. If both choose not to expand, revenues will be unchanged. If one firm chooses to expand while the other does not, the expanded firm will earn $1300 in extra revenues while the firm that did not expand will earn no extra revenues.
3. Decor. Durim and Palester are choosing colors for their gym. As it turns out, the colors of the two firms matter to customers (not only for their preferences, but also their ability to distinguish between the two firms). The following choices and corresponding hourly profits apply:
