Customer’s loyalty results in long-run market share of a firm, which is a base for retaining loyal customers. Marketing strategies pertaining to customer retention and customer acquisition are examined for five major global mobile service providers in Nigeria. Here we proposed a mathematical model to explore firm market share analysis, customer retention and switching rate. The customer retention rate and switching rate would be assumed in the model to be constant from time to time because of our underlying assumption that our Markov models have a finite chain and with stationary transition probabilities. How these probability values will be used to compute each firm’s market share is demonstrated. Finally, we used the Markov model to design marketing strategy to raise the customer retention rate and the rate of gaining competitor’s customers.