The University of South Wisconsin has had steady enrollments over the past five years. The school has its own bookstore, called University Book Store, but there are also three private bookstores in town: Bill's Book Store, College Book Store, and Battle's Book Store. The university is concerned about the large number of students who are switching to one of the private stores. As a result, South Wisconsin's president, Andy Lange, has decided to give a student three hours of university credit to look into the problem. The following matrix of transition probabilities was obtained.
University Bill's College Battle's
University 0.6 0.2 0.1 0.1
Bill's 0 0.7 0.2 0.1
College 0.1 0.1 0.8 0
Battle's 0.05 0.05 0.1 0.8
At the present time, each of the four bookstores has an equal share of the market. What will the market shares be for the next period?