I am trying to estimate the distribution of market share based on current market share and incorporating switching probability.
Consider 2 Coffee chains - Starbucks and Pret.
Each day there is 20% chance that a customer switches from Starbucks to Pret A Manger and 10% chance that a customer switches from Pret to Starbucks.
Current Market share = [.4,.6] Switching probability = [[.8,.2][.1,.9]]
How do I calculate the final market share distribution?