A Local Business a Has Two Competitors, B and C

question 134

Multiple Choice

A local business A has two competitors, B and C. No customer patronizes more than one of these businesses at the same time. Initially, the probabilities that a customer patronizes A, B, or C are 0.2, 0.6, and 0.2, respectively. Suppose A initiates an advertising campaign to improve its business and finds the following transition matrix to describe the effect. ​ ​
Find the steady-state vector for this market-that is, the long-range share of the market that each business can expect if the transition matrix holds.
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Definitions:

Illusion

A misperception or misinterpretation of a real external stimulus, often influenced by the individual's emotional state.

Fireworks Display

A public exhibition of fireworks, often organized to celebrate events or festivals, displaying elaborate colors and patterns in the sky.

Posttraumatic Stress Disorder

A psychological condition that arises after someone has experienced or seen a traumatic event, leading to persistent nightmares, flashbacks, and heightened anxiety.

Eustress

Positive, beneficial stress that motivates and focuses energy, often associated with agreeable or happy events.