Markov analysis can be very helpful in predicting future states. The equilibrium conditions are determined to indicate how the future will look if things continue as in the past. In this chapter, the existence of absorbing states was presented, and the equilibrium conditions were determined when one or more of these were present.

However, it is important to remember that the future conditions found using Markov analysis are based on the assumption that the transition probabilities do not change. When using Markov analysis to predict market shares, as in the grocery store example, it should be noted that companies are constantly trying to change these probabilities so that their own market shares increase. This was illustrated in the Modeling in the Real World vignette about Finnair, which was using ­Markov analysis to help measure its success in retaining customers. When one company succeeds in changing the transition probabilities, other companies will respond and try to move the probabilities in a direction more favorable to them. At times, new companies enter the market, and this changes the dynamics (and probabilities) as well.

In the accounts receivable example on absorbing states, future revenues were predicted based on existing probabilities. However, things can certainly change due to factors that are controllable, as well as factors that are not controllable. The financial crisis throughout the United States in 2007–2009 is a good example of this. Some banks and other lending institutions had been making loans that were less secure than the ones they had made in the past. Many mortgages, which were reliable sources of income for the banks when housing prices were rapidly rising, were becoming problematic when housing prices began to fall. The economy as a whole was in decline, and individuals who became unemployed were having trouble repaying their loans. Thus, the future conditions (and revenues) that were expected if probabilities did not change were never realized. It is important to remember the assumptions behind all these models.