Question

over any goven month, Oasis Corporation loses 10% of its customers to Glitter Glow inc. and...

over any goven month, Oasis Corporation loses 10% of its customers to Glitter Glow inc. and 20% of its market to Arik Air. But Glitter Glow Inc. loses 5% of its market to Oasis and 10% if its market to Arik Air each month; and Arik Air loses 5% of its market to Glitter Glow and 5% of its market to oasis corporation. At the present time, each of these organizations has an equal share of the market.

a.what do you think the market shares will be next month

B. what will they find in 3 months

Math   Statistics-And-Probability   
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Answer #1

P <- matrix(c(0.7,0.1,0.2,0.05,0.85,0.1,0.05,0.05,0.9),nrow=3,byrow =T)
P
I = c(1/3 ,1/3,1/3)
I %*%    P
I %*% (P %^% 3)

P
     [,1] [,2] [,3]
[1,] 0.70 0.10  0.2
[2,] 0.05 0.85  0.1
[3,] 0.05 0.05  0.9
> I = c(1/3 ,1/3,1/3)
> I %*%    P
          [,1]      [,2] [,3]
[1,] 0.2666667 0.3333333  0.4
> I %*%  (P %^% 3)
          [,1]      [,2]      [,3]
[1,] 0.1951667 0.3251667 0.4796667

hence

a) 26.67 % Oasis , 33.33% Glitter Glow , 40 % Arik

b) 19.52 % Oasis , 32.52% Glitter Glow , 47.97 % Arik

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