Question 2 (20 marks) Consider a resource allocation setting in which n agents have positive additive...

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Question 2 (20 marks) Consider a resource allocation setting in which n agents have positive additive utilities over m>n indivisible items. Prove or disprove the following statements. The allocation that maximizes utilitarian welfare is Pareto optimal. If an allocation is Pareto optimal, it is envy-free. If n = 2, envy-freeness and proportionality are equivalent. The sequential allocation algorithm, in which agents arrive in order (1,2,3,...,n)* and are given a most preferred unallocated item, is strategyproof. Question 2 (20 marks) Consider a resource allocation setting in which n agents have positive additive utilities over m>n indivisible items. Prove or disprove the following statements. The allocation that maximizes utilitarian welfare is Pareto optimal. If an allocation is Pareto optimal, it is envy-free. If n = 2, envy-freeness and proportionality are equivalent. The sequential allocation algorithm, in which agents arrive in order (1,2,3,...,n)* and are given a most preferred unallocated item, is strategyproof.