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

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## 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 \(\frac{n-q}{n^{2}-n}\) is uniquely achieved by the following simple allocation rule: assign one object to each of the \(q-1\) agents with the highest valuations, a large probability to the agent with the *q*th highest valuation, and the remaining probability to the agent with the \((q+1)\)th highest valuation.

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