Caragiannis, Ioannis and Voudouris, Alexandros (2021) The efficiency of resource allocation mechanisms for budget-constrained users. Mathematics of Operations Research, 46 (2). pp. 503-523. DOI https://doi.org/10.1287/moor.2020.1070
Caragiannis, Ioannis and Voudouris, Alexandros (2021) The efficiency of resource allocation mechanisms for budget-constrained users. Mathematics of Operations Research, 46 (2). pp. 503-523. DOI https://doi.org/10.1287/moor.2020.1070
Caragiannis, Ioannis and Voudouris, Alexandros (2021) The efficiency of resource allocation mechanisms for budget-constrained users. Mathematics of Operations Research, 46 (2). pp. 503-523. DOI https://doi.org/10.1287/moor.2020.1070
Abstract
We study the effciency of mechanisms for allocating a divisible resource. Given scalar signals submitted by all users, such a mechanism decides the fraction of the resource that each user will receive and a payment that will be collected from her. Users are self-interested and aim to maximize their utility (defined as their value for the resource fraction they receive minus their payment). Starting with the seminal work of Johari and Tsitsiklis [Mathematics of Operations Research, 2004], a long list of papers studied the price of anarchy (in terms of the social welfare - the total users’ value) of resource allocation mechanisms for a variety of allocation and payment rules. Here, we further assume that each user has a budget constraint that invalidates strategies that yield a payment that is higher than the user’s budget. This subtle assumption, which is arguably more realistic, constitutes the traditional price of anarchy analysis meaningless as the set of equilibria may change drastically and their social welfare can be arbitrarily far from optimal. Instead, we study the price of anarchy using the liquid welfare benchmark that measures effciency taking budget constraints into account. We show a tight bound of 2 on the liquid price of anarchy of the well-known Kelly mechanism and prove that this result is essentially best possible among all multi-user resource allocation mechanisms. This comes in sharp contrast to the no-budget setting where there are mechanisms that considerably outperform Kelly in terms of social welfare and even achieve full effciency. In our proofs, we exploit the particular structure of worst-case games and equilibria, which also allows us to design (nearly) optimal two-player mechanisms by solving simple differential equations.
Item Type: | Article |
---|---|
Uncontrolled Keywords: | resource allocation; liquid welfare; price of anarchy |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 17 Apr 2020 13:27 |
Last Modified: | 16 May 2024 20:18 |
URI: | http://repository.essex.ac.uk/id/eprint/27262 |
Available files
Filename: 1707.03551.pdf