Regarding the state space mentioned in the solution for the above mentioned question, I was wondering whether there should be 9 states instead of 6. The question says, "The terms of engagement of each of the audit firms require that a minimum of two annual audits must be conducted by the newly appointed firm." As I interpret this question as company is locked with the new auditor for 2 years ( solution to part 1 of this question also confirms to this interpretation), I feel the state space should be A1, A2, A, B1, B2, B, C1, C2, C where A_i would denote the company is locked with auditor A in the ith year ( i = 1,2) and so on for B and C instead of whats given in the examiners solution. This 9 state space solution would give a different answer to the stationary distribution than the six state space solution. Also noting that examiners solution mentions "The transition probabilities depend on whether it is the first year with the current auditors, so need additional states to cover this." This leads to the direction where examiners are interpreting that the company's auditor is locked only for 1 year and not 2 years. Can anyone clarify this?
I conceive that the given six states are correct. As its mandatory for company to get audited for minimum ( exact ) 2 years by respective firm, means company can not change auditor for 2 years after selected. Now, if 1st audit is by say firm A then second year audit also should by A. i.e state \(A_l\) audited by A in 1st year and then state \(A\) to audited in second year. Auditing in 1st year, then in 2nd year gives option to choose other firms for subsequent years.
Let me frame the question differently. As per examiners solution, Say at time 0 the process starts in state A_L, so it is certain that the process will move to state A at time 1 ( as per transition matrix ). Now at time 2 it is not necessary that the auditor A will remain as transitions are possible from state A to B_L and C_L which contradicts the question which requires that the auditor must be locked for at least 2 years.
