Chapter 9.2, Problem 59E

Market share. Consumers can choose between three long distance telephone services: GTT, NCJ, and Dash. Aggressive marketing by all three companies results in a continual shift of customers among the three services. Each year. GTT loses $5\%$ of its customers to NCJ and $20\%$ to Dash. NCJ loses $15\%$ of its customers to GTT and $10\%$ to Dash, and Dash loses $5\%$ 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?