标题： 测度空间上的演化博弈论：适定性 显示英文标题

标题： Evolutionary Game Theory on Measure Spaces: Well-Posedness

摘要： 试图找到一个全面的数学框架，以研究完全非线性演化博弈理论模型的适定性和渐近分析问题。 该模型应足够丰富，以包含所有经典非线性项，例如 Beverton-Holt 或 Ricker 类型。 对于在可积函数空间上制定的几种此类模型，已知当收益核的方差变小时，解在长期内收敛到以最适应策略为中心的狄拉克测度；因此，解的极限不在可积函数的状态空间中。 从复制者-突变方程和广义逻辑斯蒂方程作为基础，制定了一般模型，作为有限有符号测度状态空间上的动力系统。 建立了适定性，然后表明通过选择适当的收益核，该模型包括所有经典密度模型，包括选择和突变，以及离散和连续策略（特征）空间。 显示英文摘要

摘要： An attempt is made to find a comprehensive mathematical framework in which to investigate the problems of well-posedness and asymptotic analysis for fully nonlinear evolutionary game theoretic models. The model should be rich enough to include all classical nonlinearities, e.g., Beverton-Holt or Ricker type. For several such models formulated on the space of integrable functions, it is known that as the variance of the payoff kernel becomes small the solution converges in the long term to a Dirac measure centered at the fittest strategy; thus the limit of the solution is not in the state space of integrable functions. Starting with the replicator-mutator equation and a generalized logistic equation as bases, a general model is formulated as a dynamical system on the state space of finite signed measures. Well-posedness is established, and then it is shown that by choosing appropriate payoff kernels this model includes all classical density models, both selection and mutation, and discrete and continuous strategy (trait) spaces.