Abstract
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, noregret 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 tradeoff 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.
BibTeX  Entry
@InProceedings{gemici_et_al:LIPIcs:2019:10270,
author = {Kurtulus Gemici and Elias Koutsoupias and Barnab{\'e} Monnot and Christos H. Papadimitriou and Georgios Piliouras},
title = {{Wealth Inequality and the Price of Anarchy}},
booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
pages = {31:131:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771009},
ISSN = {18688969},
year = {2019},
volume = {126},
editor = {Rolf Niedermeier and Christophe Paul},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10270},
doi = {10.4230/LIPIcs.STACS.2019.31},
annote = {Keywords: congestion games, inequality}
}
Keywords: 

congestion games, inequality 
Seminar: 

36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019) 
Issue Date: 

2019 
Date of publication: 

12.03.2019 