Wealth Inequality and the Price of Anarchy

Authors Kurtuluş Gemici, Elias Koutsoupias, Barnabé Monnot, Christos H. Papadimitriou, Georgios Piliouras

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Kurtuluş Gemici
  • Department of Sociology, National University of Singapore, Singapore
Elias Koutsoupias
  • Department of Computer Science, University of Oxford, United Kingdom
Barnabé Monnot
  • Engineering Systems & Design, Singapore University of Technology and Design, Singapore
Christos H. Papadimitriou
  • Department of Computer Science, Columbia University, United States of America
Georgios Piliouras
  • Engineering Systems & Design, Singapore University of Technology and Design, Singapore


Kurtuluş Gemici acknowledges NUS Strategic Research Grant (WBS: R-109-000-183-646) awarded to Global Production Networks Centre (GPN@NUS). Elias Koutsoupias acknowledges ERC Advanced Grant 321171 (ALGAME). Barnabé Monnot acknowledges the SUTD Presidential Graduate Fellowship. Christos Papadimitriou acknowledges NSF grant 1408635 "Algorithmic Explorations of Networks, Markets, Evolution, and the Brain". Georgios Piliouras acknowledges SUTD grant SRG ESD 2015 097, MOE AcRF Tier 2 Grant 2016-T2-1-170, NRF grant NRF2016NCR-NCR002-028 and a NRF fellowship. Barnabé Monnot and Georgios Piliouras would like to thank the other members of the National Science Experiment team at SUTD: Garvit Bansal, Francisco Benita, Sarah Nadiawati, Hugh Tay Keng Liang, Nils Ole Tippenhauer, Bige Tunçer, Darshan Virupashka, Erik Wilhelm and Yuren Zhou. The National Science Experiment is supported by the Singapore National Research Foundation (NRF), Grant RGNRF1402.

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Kurtuluş Gemici, Elias Koutsoupias, Barnabé Monnot, Christos H. Papadimitriou, and Georgios Piliouras. Wealth Inequality and the Price of Anarchy. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


The price of anarchy quantifies the degradation of social welfare in games due to the lack of a centralized authority that can enforce the optimal outcome. It is known that, in certain games, such effects can be ameliorated via tolls or taxes. This leads to a natural, but largely unexplored, question: what is the effect of such transfers on social inequality? We study this question in nonatomic congestion games, arguably one of the most thoroughly studied settings from the perspective of the price of anarchy. We introduce a new model that incorporates the income distribution of the population and captures the income elasticity of travel time (i.e., how does loss of time translate to lost income). This allows us to argue about the equality of wealth distribution both before and after employing a mechanism. We establish that, under reasonable assumptions, tolls always increase inequality in symmetric congestion games under any reasonable metric of inequality such as the Gini index. We introduce the inequity index, a novel measure for quantifying the magnitude of these forces towards a more unbalanced wealth distribution and show it has good normative properties (robustness to scaling of income, no-regret learning). We analyze inequity both in theoretical settings (Pigou’s network under various wealth distributions) as well as experimental ones (based on a large scale field experiment in Singapore). Finally, we provide an algorithm for computing optimal tolls for any point of the trade-off of relative importance of efficiency and equality. We conclude with a discussion of our findings in the context of theories of justice as developed in contemporary social sciences and present several directions for future research.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • congestion games
  • inequality


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