多类Schelling博弈中依赖密度与亲和性的社会隔离及套利均衡
Density and Affinity Dependent Social Segregation and Arbitrage Equilibrium in a Multi-class Schelling Game
AI总结：
针对高密度城市反而社会隔离更强的反常识现象，本文提出多类Schelling博弈的博弈论模型，解释密度依赖隔离的解析条件，提出套利均衡下智能体有效效用相等的结论，为理解社会动态提供数学支撑。
摘要：
与“规模更大、密度更高的城市会促进社会经济融合”这一普遍认可的假说相反，近期一项研究（Nilforoshan等人，2023）报告了相反的结果，即隔离程度更高。本文提出一个博弈论模型，可在单类和双类系统中预测这种依赖密度的隔离结果，该模型为导致该现象的解析条件提供了关键洞见。此外，套利均衡结果意味着所有智能体的有效效用相等，这可被解释为在我们的理想社会中，所有智能体在各自环境中都同等“幸福”。我们认为该模型有助于深化对社会动态与行为的数学理解，这对我们努力构建更和谐的社会具有重要意义。
英文摘要：
Contrary to the widely believed hypothesis that larger, denser cities promote socioeconomic mixing, a recent study (Nilforoshan et al. 2023) reports the opposite behavior, i.e. more segregation. Here, we present a game-theoretic model that predicts such a density-dependent segregation outcome in both one- and two-class systems. The model provides key insights into the analytical conditions that lead to such behavior. Furthermore, the arbitrage equilibrium outcome implies the equality of effective utilities among all agents. This could be interpreted as all agents being equally "happy" in their respective environments in our ideal society. We believe that our model contributes towards a deeper mathematical understanding of social dynamics and behavior, which is important as we strive to develop more harmonious societies.
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