Cities at Play: Improving Equilibria in Urban Neighbourhood Games

TL;DR

This paper models strategic urban neighborhood choices using game theory, showing that small, targeted investments can significantly improve social welfare by aligning individual incentives with societal goals.

Contribution

It introduces a game-theoretic model of neighborhood selection and demonstrates how carefully designed interventions can guarantee improved social welfare at minimal cost.

Findings

Small-scale utility modifications can ensure Nash equilibria with high social welfare

Targeted investments at a cost of at most 0.81 epsilon squared times the optimal can guarantee epsilon times the optimal welfare

The approach formalizes how strategic interventions can turn negative outcomes into positive societal benefits

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.