In an organization, A1 prefers three (3) tasks T3, T2, and T1 in order of preference. A2 prefers the three (3) tasks as follows T2, T3, and T1. A3 prefers the three (3) tasks as follows T2, T3, and T1, the same as A2. The owner P has assessed the competency of each agent to do each task in order of ability as follows. For T1, the best agents in order are A1, A2, and A3. For T2, the best agents in order are A1, A2, and A3, the same as T1. For T3, the best agents in order are A2, A1, and A3. Each Agent can only do one task.
(a) How could P match each agent to each task optimally?
(b) Why can this algorithm be said to be efficient as well as satisfying the total value maximization principle?
(c) What happens if A2 misrepresents its preferences as T2, T1, and T3, instead of T2, T3, and T1?