Diversity-seeking swap games in networks

TL;DR

This paper introduces diversity-seeking swap games in networks, analyzing how different utility functions influence segregation and diversity measures, with theoretical bounds and simulations showing the effectiveness of diversity-seeking behaviors.

Contribution

It proposes new swap game models based on diversity-seeking utilities and provides theoretical bounds on their efficiency and extensive simulation results.

Findings

Diversity-seeking agents reduce segregation effectively.

Strong diversity measures are harder to achieve.

Theoretical bounds align with simulation outcomes.

Abstract

Schelling games use a game-theoretic approach to study the phenomenon of residential segregation as originally modeled by Schelling. Inspired by the recent increase in the number of people and businesses preferring and promoting diversity, we propose swap games under three diversity-seeking utility functions: the binary utility of an agent is 1 if it has a neighbor of a different type, and 0 otherwise; the difference-seeking utility of an agent is equal to the number of its neighbors of a different type; the variety-seeking utility of an agent is equal to the number of types different from its own in its neighborhood. We consider four global measures of diversity: degree of integration, number of colorful edges, neighborhood variety, and evenness, and prove asymptotically tight or almost tight bounds on the price of anarchy with respect to these measures on both general graphs, as well as on cycles, cylinders, and tori that model residential neighborhoods. We complement our theoretical results with simulations of our swap games starting either from random placements of agents, or from segregated placements. Our simulation results are generally consistent with our theoretical results, showing that segregation is effectively removed when agents are diversity-seeking; however strong diversity, such as measured by neighborhood variety and evenness, is harder to achieve by our swap games.