Matching Markets

TL;DR

This paper explores the extension of matching market theory to more complex scenarios, including indivisible goods and dynamic preferences, aiming to improve resource allocation models in economics and computer science.

Contribution

It introduces new research directions for modeling matching markets with complex preferences and discusses computational challenges and solutions.

Findings

Polynomial algorithms for divisible goods with linear utilities

NP-hardness of finding market clearing prices for indivisible goods

Potential for modeling dynamic buyer preferences

Abstract

Matching markets are of particular interest in computer science and economics literature as they are often used to model real-world phenomena where we aim to equitably distribute a limited amount of resources to multiple agents and determine these distributions efficiently. Although it has been shown that finding market clearing prices for Fisher markets with indivisible goods is NP-hard, there exist polynomial-time algorithms able to compute these prices and allocations when the goods are divisible and the utility functions are linear. We provide a promising research direction toward the development of a market that simulates buyers' preferences that vary according to the bundles of goods allocated to other buyers. Our research aims to elucidate unique ways in which the theory of matching markets can be extended to account for more complex and often counterintuitive microeconomic phenomena.