Diversity-seeking swap games in networks

2025-02-19

AI Summary

This paper investigates diversity-seeking Schelling exchange games to mitigate residential segregation. We propose three novel utility functions—binary, difference-based, and variety-seeking—to formally capture agents’ proactive preference for heterogeneous neighbors. To quantify system-wide diversity, we introduce a four-dimensional global metric integrating integration level, number of chromatic edges, neighborhood diversity, and balance. We establish the first tight theoretical bound on the Price of Anarchy (PoA) for such games. Our PoA bounds are nearly tight on general graphs as well as on periodic and toroidal topologies. Large-scale simulations demonstrate that the mechanism effectively eliminates segregation; however, a fundamental trade-off emerges between neighborhood diversity and balance. Key contributions include: (i) the first formal framework for diversity-seeking exchange dynamics; (ii) unified multi-scale modeling of diversity—from local neighborhoods to global structure; and (iii) rigorous theoretical analysis yielding tight PoA guarantees.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Fair Division
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Study diversity-seeking in swap games
• Analyze utility functions for diversity
• Measure segregation reduction in networks

Innovation

• Diversity-seeking utility functions
• Global diversity measures analysis
• Simulation of swap games effectiveness