Cities at Play: Improving Equilibria in Urban Neighbourhood Games

2026-01-13

AI Summary

This study investigates how cities can employ low-cost interventions to steer individuals’ strategic choices within local environments, thereby enhancing overall social welfare and mitigating efficiency losses caused by self-interested behavior. Building upon Schelling’s bounded-neighborhood model, the work introduces Braess’s paradox into the context of neighborhood selection and formulates a game-theoretic framework under non-monotonic concave utility functions. By applying minimal, targeted adjustments to individual local utilities, the intervention aligns Nash equilibria with near-optimal social outcomes. Theoretically, it is proven that when the total intervention cost does not exceed \(0.81\varepsilon^2 \cdot \text{opt}\), all resulting Nash equilibria guarantee social welfare of at least \(\varepsilon \cdot \text{opt}\). This provides urban planners with a quantifiable, theoretically grounded incentive mechanism for strategic city design.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Search and Optimization: Local Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

How should cities invest to improve social welfare when individuals respond strategically to local conditions? We model this question using a game-theoretic version of Schelling's bounded neighbourhood model, where agents choose neighbourhoods based on concave, non-monotonic utility functions reflecting local population. While naive improvements may worsen outcomes - analogous to Braess'paradox - we show that carefully designed, small-scale investments can reliably align individual incentives with societal goals. Specifically, modifying utilities at a total cost of at most $0.81 \epsilon^2 \cdot \texttt{opt}$ guarantees that every resulting Nash equilibrium achieves a social welfare of at least $\epsilon \cdot \texttt{opt}$, where $\texttt{opt}$ is the optimum social welfare. Our results formalise how targeted interventions can transform supra-negative outcomes into supra-positive returns, offering new insights into strategic urban planning and decentralised collective behaviour.

Problem

• urban planning
• strategic behavior
• social welfare
• Nash equilibrium
• Schelling model

Innovation

• urban neighbourhood games
• targeted intervention
• Nash equilibrium
• social welfare optimization
• Braess-like paradox