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    Market Share and Markov Chains
    A Markov chain is a simple concept which can explain and model complicated real time processes. A simple Markov chain is based upon the premise that the next state in the process only depends upon the previous state and that the probabilities to change from state to state remain fixed (constant) at all time.
    In this project lets assume that you are an analyst in a market research company who has been hired to examine which cola company another soda company should merge with in the future. The soda company wishes to join that cola company which will have the largest market share in the future.
    Coke Pepsi and RC Cola are the only cola companies in operation and the ones which are being considered for the merger. Currently (at time zero) Pepsi owns 45% of market share Coke owns 33% of market share and RC Cola owns 22% of market share.
    As you start your analysis you find that individual customers change their preferences or choices for cola drinks over each month and find that:
    The following diagram depicts the changing preference transitions of cola customers during a one month transition reflecting the information above:
    The notation

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