Assignment task: Please be as detailed when providing solution:
This issue addresses the multi-object allocation issue.
Most sports leagues use a draught to choose players for teams. Importantly, they do not (at least directly) consider the preferences of the participants. As a result, we may represent this as a problem of multi-object allocation in which the players are the "objects" and the teams are the "individuals." For instance, the NFL draught has 32 teams and a large number of athletes. The right to seven draught choices each team. Each team selects one player in each of the first seven rounds of the draught. Each time they choose, they do it in the same sequence.
Show that the draft rule is neither Pareto efficient nor strategy proof even if teams' preferences are responsive. You can pick any number of teams and players as you need to prove this. Moreover, you can list the teams as i1,i2,... so that i1 picks first, i2 picks second, and so on, in each round.
(Hint: you don't need to construct examples with 32 teams. Just two teams suffice to produce a counterexample to Pareto efficiency and strategyproofness)
Note: Please use a set of individuals, set of objects and a profile preference to demonstrate/prove the question.