Advertising
Use the following information for Problem. A local business A has two competitors, B and C. No customer patronizes more than one of these businesses at the same time. Initially the probabilities that a customer patronizes A, B, or C are 0.2, 0.6, and 0.2, respectively. Suppose A initiates an advertising campaign to improve its business and finds the following transition matrix to describe the effect.
Find the steady-state vector for this market-that is, the long-range share of the market that each business can expect if the transition matrix holds.