Wealth Inequality and the Price of Anarchy

TL;DR

This paper investigates how mechanism design, specifically tolls in congestion games, affects wealth inequality, revealing that tolls tend to increase inequality and proposing measures and algorithms to balance efficiency and fairness.

Contribution

It introduces a new model incorporating wealth distribution into congestion games, analyzes the impact of tolls on inequality, and develops algorithms for optimal toll design balancing efficiency and equality.

Findings

Tolls increase inequality in symmetric congestion games under common metrics.

The iniquity index effectively measures the impact of mechanisms on wealth disparity.

Algorithms are provided for computing tolls that optimize the trade-off between efficiency and fairness.

Abstract

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. At its antipodes, mechanism design studies how to ameliorate these effects by incentivizing socially desirable behavior and implementing the optimal state as equilibrium. In practice, the responsiveness to such measures depends on the wealth of each individual. This leads to a natural, but largely unexplored, question. Does optimal mechanism design entrench, or maybe even exacerbate, social inequality? We study this question in nonatomic congestion games, arguably one of the most thoroughly studied settings from the perspectives of price of anarchy as well as mechanism design. We introduce a new model that incorporates the wealth distribution of the population and captures the income elasticity of travel time. This allows us to argue about the equality of wealth distribution both before and after employing a mechanism. We start our analysis by establishing a broad qualitative result, showing that tolls always increase inequality in symmetric congestion games under any reasonable metric of inequality, e.g., the Gini index. Next, we introduce the iniquity 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 iniquity 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.