# Redistribution Mechanisms for Assignment of Heterogeneous Objects

arXiv: https://arxiv.org/abs/1401.3884 · HTML: https://mlsanity.com/paper/1401.3884/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2014.

## Built on by (most cited first, 1 of 1)

- [Achieving PAC Guarantees in Mechanism Design through Multi-Armed Bandits](https://mlsanity.com/paper/2412.00345/) (2024)

## Abstract (arXiv)

There are p heterogeneous objects to be assigned to n competing agents (n > p) each with unit demand. It is required to design a Groves mechanism for this assignment problem satisfying weak budget balance, individual rationality, and minimizing the budget imbalance. This calls for designing an appropriate rebate function. When the objects are identical, this problem has been solved which we refer as WCO mechanism. We measure the performance of such mechanisms by the redistribution index. We first prove an impossibility theorem which rules out linear rebate functions with non-zero redistribution index in heterogeneous object assignment. Motivated by this theorem, we explore two approaches to get around this impossibility. In the first approach, we show that linear rebate functions with non-zero redistribution index are possible when the valuations for the objects have a certain type of relationship and we design a mechanism with linear rebate function that is worst case optimal. In the second approach, we show that rebate functions with non-zero efficiency are possible if linearity is relaxed. We extend the rebate functions of the WCO mechanism to heterogeneous objects assignment and conjecture them to be worst case optimal.