In an organization, A1 prefers three (3) tasks T3, T2, and T1 in order of prefer

Question

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?

Explanation / Answer

assume that choose out of best 2 out of 3 whether preferences or ability

ACC TO ABILITY;

T1=A1 THEN A2 THEN A3

T2=A1 THEN A2 THEN A3

T3=A2 THEN A1 THEN A3   

NOW consider preferences in parts

(a) A3 has equal ability in each task but his preference is T2 so assign T2 to A3

then T1 to A1, T3 to A2

(b) According to TVM, If there are no wealth effects (with respect to individuals' preferences), an arrangement is efficient only if it maximizes total value with respect to these individuals.

So this theorem satisfy TVM

(c) so in that case there are 2 solutions

CASE 1 T3 to A1 ,T2 to A2, T1 TO A3

CASE 2 T3 to A3 ,T2 TO A2,T1 to A1

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.