中文摘要
犯罪的空间异质性表明，区位是犯罪行为与警力配置中的关键选择变量。为刻画这一点，我们构建了一个犯罪者与警察在空间上策略互动的拓扑模型。与现有文献的关键区别在于距离的作用：一个警力单元的覆盖半径会产生空间溢出，因此某一区位可以从邻近巡逻中获得保护。这与离散空间模型形成鲜明对比——在后者中，每个单元与周边相互隔离，从而使均衡警力配置产生偏误，并忽视了生态谬误的一种形式。我们解析地刻画了这一偏误，并更一般地论证了溢出如何影响均衡警力配置。特别地，随着溢出增加：(i) 在犯罪的局部极大值（极小值）处配置更多（更少）的警力单元；(ii) 警力单元更为集中的区位向犯罪分布最陡峭的一侧移动；(iii) 警力空间密度的熵下降。综合来看，我们的结果指向空间溢出在犯罪与警力配置的均衡决定中的核心作用。
Abstract
Spatial heterogeneity in crime suggests that location is a key choice variable in criminal behavior and police allocation. To capture this, we develop a topological model in which criminals and the police interact strategically across space. The key departure from the existing literature is that distance matters: the coverage radius of a police unit generates spatial spillovers, so a location can receive protection from nearby patrols. This is in sharp contrast with discrete spatial models, where each cell is isolated from its surroundings, biasing the equilibrium police allocation and overlooking a form of the ecological fallacy. We analytically characterize this bias and, more generally, demonstrate how spillovers affect the equilibrium police allocation. In particular, as spillovers increase: (i) more (fewer) units are allocated at local maxima (minima) of crime; (ii) the location where units are more concentrated shifts toward the steepest side of the crime distribution; and (iii) the entropy of the police spatial density decreases. Jointly, our results point to the essential role of spatial spillovers in the equilibrium determination of crime and police allocation.