Social gravity law widely exists in human travel, population migration, commodity trade, information communication, scientific collaboration and so on. Why is there such a simple law in many complex social systems is an interesting question. Although scientists from fields of statistical physics, complex systems, economics and transportation science have explained the social gravity law, a theoretical explanation including two dominant mechanisms, namely individual interaction and bounded rationality, is still lacking. Here we present a free utility model from the perspective of individual choice behavior to explain the social gravity law. The basic assumption is that bounded rational individuals interacting with each other will trade off the expected utility and information-processing cost to maximize their own utility. The previous explanations of the social gravity law including the maximum entropy model, the free cost model, the Logit model and the destination choice game model are all special cases under our model. Further, we extend the free utility model to the dummy network and real transportation network. This model not only helps us to better understand the underlying mechanisms of spatial interaction patterns in complex social systems, but also provides a new perspective for understanding the potential function in game theory and the user equilibrium model in transportation science.

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解释社会万有引力定律的免费实用新型

社会引力定律广泛存在于人类旅行、人口迁移、商品贸易、信息交流、科学合作等领域。为什么在许多复杂的社会系统中会有如此简单的规律是一个有趣的问题。尽管统计物理、复杂系统、经济学和交通科学等领域的科学家已经对社会引力定律进行了解释，但仍然缺乏包括个体相互作用和有限理性两种主导机制的理论解释。在这里，我们提出一个从个人选择行为的角度来解释社会引力定律的自由实用新型。基本假设是，有限理性个体之间的相互作用将在预期效用和信息处理成本之间进行权衡，以最大化他们自己的效用。前面对社会引力定律的解释包括最大熵模型、自由成本模型、Logit 模型和目的地选择博弈模型，都是我们模型下的特例。此外，我们将免费实用新型扩展到虚拟网络和真实交通网络。该模型不仅有助于我们更好地理解复杂社会系统中空间交互模式的潜在机制，而且为理解博弈论中的势函数和交通科学中的用户均衡模型提供了新的视角。