Conference proceeding
Nash SocialWelfare Approximation for Strategic Agents
EC'17: PROCEEDINGS OF THE 2017 ACM CONFERENCE ON ECONOMICS AND COMPUTATION, pp 611-628
01 Jan 2017
Abstract
The fair division of resources among strategic agents is an important age-old problem that has led to a rich body of literature. At the center of this literature lies the question of whether there exist mechanisms that can implement fair outcomes, despite the agents' strategic behavior. A fundamental objective function used for measuring the fairness of an allocation is the geometric mean of the agents' values, known as the Nash social welfare (NSW). This objective function is maximized by widely known solution concepts such as Nash bargaining and the competitive equilibrium with equal incomes.
In this work we focus on the question of (approximately) implementing this objective. The starting point of our analysis is the Fisher market, a fundamental model of an economy, whose benchmark is precisely the (weighted) Nash social welfare. We begin by studying two extreme classes of valuations functions, namely perfect substitutes and perfect complements, and find that for perfect substitutes, the Fisher market mechanism yields a constant approximation: at most 2 and at least e(1/e) (approximate to 1.44). However, for perfect complements, the Fisher market mechanism does not work well, its bound degrading linearly with the number of players.
Strikingly, the Trading Post mechanism-an indirect market mechanism also known as the Shapley-Shubik game-has significantly better performance than the Fisher market on its own benchmark. Not only does Trading Post achieve an approximation of 2 for perfect substitutes, but this bound holds for any concave utilities, and it becomes essentially optimal for perfect complements, where it reaches (1 + epsilon) for any epsilon > 0. Moreover, we show that all the Nash equilibria of the Trading Post mechanism are pure (hence the approximation factors extend to all Nash equilibria), and satisfy an important notion of individual fairness known as proportionality.
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Details
- Title
- Nash SocialWelfare Approximation for Strategic Agents
- Creators
- Simina Branzei - Hebrew University of JerusalemVasilis Gkatzelis - Drexel UniversityRuta Mehta - University of Illinois Urbana-ChampaignAssoc Comp Machinery
- Publication Details
- EC'17: PROCEEDINGS OF THE 2017 ACM CONFERENCE ON ECONOMICS AND COMPUTATION, pp 611-628
- Publisher
- Assoc Computing Machinery
- Number of pages
- 18
- Grant note
- I-CORE Program of the Planning and Budgeting Committee CCF-1408635; CCF-1216073; CCF-1161813 / NSF; National Science Foundation (NSF) 740282 / European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme; European Research Council (ERC) 2014389 / Israel-USA Bi-national Science Foundation (BSF); US-Israel Binational Science Foundation Israel Science Foundation 1435/14 / ISF; Israel Science Foundation
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- Computer Science
- Web of Science ID
- WOS:000628648900066
- Scopus ID
- 2-s2.0-85025825378
- Other Identifier
- 991019302292004721
InCites Highlights
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Computer Science, Artificial Intelligence
- Computer Science, Theory & Methods
- Economics
- Mathematics, Applied
- Operations Research & Management Science