# Envy-free and budget-balanced assignment of identical objects

Yan Long ()
Yan Long: New York University Abu Dhabi

Social Choice and Welfare, 2018, vol. 50, issue 4, 705-719

Abstract: Abstract Strategy-proof, budget-balanced, and envy-free rank mechanisms assign q identical objects to n agents. The efficiency loss is the largest ratio of surplus loss to efficient surplus, over all profiles of non-zero valuations. The smallest efficiency loss $$\frac{n-q}{n^{2}-n}$$ n - q n 2 - n is uniquely achieved by the following simple allocation rule: assign one object to each of the $$q-1$$ q - 1 agents with the highest valuations, a large probability to the agent with the qth highest valuation, and the remaining probability to the agent with the $$(q+1)$$ ( q + 1 ) th highest valuation.

Date: 2018
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