Cities at Play: Improving Equilibria in Urban Neighbourhood Games
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911372313362432 |
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| author | Gairing, Martin Vetta, Adrian Zhao, Zhanzhan |
| author_facet | Gairing, Martin Vetta, Adrian Zhao, Zhanzhan |
| contents | 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 $0.81 ε^2 \cdot \texttt{opt}$ guarantees that every resulting Nash equilibrium achieves a social welfare of at least $ε\cdot \texttt{opt}$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cities at Play: Improving Equilibria in Urban Neighbourhood Games Gairing, Martin Vetta, Adrian Zhao, Zhanzhan Computer Science and Game Theory Theoretical Economics 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 $0.81 ε^2 \cdot \texttt{opt}$ guarantees that every resulting Nash equilibrium achieves a social welfare of at least $ε\cdot \texttt{opt}$, 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. |
| title | Cities at Play: Improving Equilibria in Urban Neighbourhood Games |
| topic | Computer Science and Game Theory Theoretical Economics |
| url | https://arxiv.org/abs/2601.08642 |