Consumers in a certain state choose between three long distance telephone servic

Question

Consumers in a certain state choose between three long distance telephone services. GTT, NCJ, and Dash. Aggressive marketing by all three companies results in a continual shift of customers among the three services. Each year, GTT loses 30% of its customers to NCJ and 20% to Dash, NCJ loses 15% of its customers to GTT and 5% to Dash, and Dash loses 5% of its customers to GTT and 30% to NCJ. Assuming that these percentages remain valid over a long period of time, what is each company's expected market share in the long run?

Explanation / Answer

........ GTT NCJ Dash
GTT 0.55 0.20 0.25
NCJ 0.05 0.85 0.10
Dash 0.30 0.30 0.40

for steady state,
0.55p +0.05q + 0.30r = p
0.20p +0.85q + 0.30r = q
0.25p +0.10q + 0.40r = r
p+q+r = 1

which yields

[ 0.192 0.624 0.184 ]

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