有限人口动力学解决检查游戏的中心悖论

检查游戏是法律执法(检查员)与公民(潜在犯罪者)之间战略冲突的典范模型。其经典混合策略纳什均衡(MSNE)存在悖论：均衡下的犯罪率独立于罚金大小($p$)和犯罪收益($g$)，削弱了威慑政策的有效性。我们使用演化博弈论重新审视这一挑战，关注有限、非对称人口规模受人口噪声影响下的策略长期固定概率。该模型的确定性极限表明，稳定的极限循环位于 MSNE 附近， coincide with the neutral fixed point of the equilibrium analysis. Crucially, in finite populations, demographic noise drives the system away from this cycle and toward absorbing states. Our results demonstrate that high absolute penalties $p$ are highly effective at suppressing crime by influencing the geometry of the deterministic dynamics, which in turn biases the fixation probability toward the criminal extinction absorbing state, thereby restoring the intuitive role of $p$. Furthermore, we reveal a U 形政策景观 where both high penalties and light penalties (where $p \approx g$) are successful suppressors, maximizing criminal risk at intermediate penalty levels. Most critically, we analyze the realistic asymptotic limit of extreme population sizes asymmetry, where inspectors are exceedingly rare. In this limit, the system's dynamic outcome is entirely decoupled from the citizen payoff parameters $p$ and $g$, and is instead determined by the initial frequency of crime relative to the deterrence threshold (the ratio of inspection cost to reward for catching a criminal). This highlights that effective crime suppression requires managing the interaction between deterministic dynamics, demographic noise, and initial conditions.