Year: 2024
Type: preprint
Abstract: The assignment game, introduced by Shapley and Shubik (1971), is a classic model for two-sided matching markets between buyers and sellers. In the original assignment game, it is assumed that payments lead to transferable utility and that buyers have unit-demand valuations for items. Two important and mostly independent lines of work have studied more general settings with imperfectly transferable utility and gross substitutes valuations. Multiple efficient algorithms have been proposed for computing a competitive equilibrium, the standard solution concept in assignment games, in these two settings. Our main result is an efficient algorithm for computing competitive equilibria in a setting with both imperfectly transferable utility and gross substitutes valuations. Our algorithm combines augmenting tree techniques from maximum matching and algorithms for matroid intersection. We also show that, in two mild generalizations of our model, computing a competitive equilibrium is NP-hard.
Source: arXiv (Cornell University)
Authors: Balkanski, Eric, En, Christopher, Faenza, Yuri
Institution: Columbia University
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4399913024