Optimization-friendly generic mechanisms without money

TL;DR

This paper introduces a flexible framework called extit{Apex} that transforms local search optimization algorithms into mechanisms for preference aggregation among self-interested agents without using monetary transfers.

Contribution

The paper presents extit{Apex}, a novel meta-algorithm enabling optimization algorithms to function as mechanisms in non-monetary preference aggregation settings, and extends classical results on competitive equilibria.

Findings

Strengthens the 1979 Hylland-Zeckhauser result on allocation via CEEI.

Shows that reweighing utilities can produce HZ-equilibrium prices with VCG.

Provides a new proof of the HZ79 result using Brouwer's fixed point theorem.

Abstract

The goal of this paper is to develop a generic framework for converting modern optimization algorithms into mechanisms where inputs come from self-interested agents. We focus on aggregating preferences from $n$ players in a context without money. Special cases of this setting include voting, allocation of items by lottery, and matching. Our key technical contribution is a new meta-algorithm we call \apex (Adaptive Pricing Equalizing Externalities). The framework is sufficiently general to be combined with any optimization algorithm that is based on local search. We outline an agenda for studying the algorithm's properties and its applications. As a special case of applying the framework to the problem of one-sided assignment with lotteries, we obtain a strengthening of the 1979 result by Hylland and Zeckhauser on allocation via a competitive equilibrium from equal incomes (CEEI). The [HZ79] result posits that there is a (fractional) allocation and a set of item prices such that the allocation is a competitive equilibrium given prices. We further show that there is always a reweighing of the players' utility values such that running unit-demand VCG with reweighed utilities leads to a HZ-equilibrium prices. Interestingly, not all HZ competitive equilibria come from VCG prices. As part of our proof, we re-prove the [HZ79] result using only Brouwer's fixed point theorem (and not the more general Kakutani's theorem). This may be of independent interest.