Inequality and Network Formation Games

TL;DR

This paper introduces the Nash Inequality Ratio (NIR) to measure inequality in network formation games and provides bounds on it, revealing that social efficiency does not always increase inequality.

Contribution

It defines the NIR for network formation games and establishes tight bounds, challenging the assumption that efficiency and inequality are inversely related.

Findings

Tight upper bounds on NIR for specific network formation games.

Inequality can be bounded independently of social efficiency.

Efficiency does not necessarily lead to increased inequality.

Abstract

This paper addresses the matter of inequality in network formation games. We employ a quantity that we are calling the Nash Inequality Ratio (NIR), defined as the maximal ratio between the highest and lowest costs incurred to individual agents in a Nash equilibrium strategy, to characterize the extent to which inequality is possible in equilibrium. We give tight upper bounds on the NIR for the network formation games of Fabrikant et al. (PODC '03) and Ehsani et al. (SPAA '11). With respect to the relationship between equality and social efficiency, we show that, contrary to common expectations, efficiency does not necessarily come at the expense of increased inequality.