Markov Chain

To understand Markov Chain, you have to know matrices and their basic operations.

As this page is designed for beginners, it is simplified. One should refer to academic text for proper terms.

Given market share matrix:

                        [0.45    0.3    0.25]

 Given transition probability matrix:

                                C        P        A

                C             0.7        0.2       0.1

                P            0.15        0.6       0.25

                A             0.1       0.25       0.65

 Explanation of the second matrix given above:

                                        For example, look at 2nd row. 0.15    0.6    0.25

Therefore, after one month the market share matrix of these 3 soft drinks is given by:

         [0.45    0.3    0.25]                 0.7        0.2       0.1

                                                   0.15        0.6       0.25

                                                   0.1       0.25       0.65

If we call the 2 matrices right above M and T. 

Then after 2 months:

         The marker share by these colas will be given by :    MTT

After 3 months:

multiply the transition probabilities again

                That is:    MTTT

After 4 months:

MTTTT

and so forth

For more details see the attached documents below:

• Brand Switching

• Aussie Cola

• Market Share

• Spread Sheet

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