Consumers in a certain state can choose between three long-distance telephone services: GTT, NCJ, and Dash. Aggressive marketing by all three companies results in continual shift of customers among the three services. Each year, GTT loses 25% of its customers to NCJ and 25% to Dash; NCJ loses 10% of its customers to GTT and 10% to Dash; and Dash loses 15% of its customers to GTT and 10% to NCJ. Assuming that these percentages remain valid over a long period of time, what is each company’s expected market share in the long run?

Question

Consumers in a certain state can choose between three long-distance telephone services:  GTT, NCJ, and Dash.  Aggressive marketing by all three companies results in continual shift of customers among the three services.  Each year, GTT loses 25% of its customers to NCJ and 25% to Dash; NCJ loses 10% of its customers to GTT and 10% to Dash; and Dash loses 15% of its customers to GTT and 10% to NCJ.  Assuming that these percentages remain valid over a long period of time, what is each company’s expected market share in the long run?