知识传播与彩票社会

Henri Berestycki, Alexei Novikov, Jean-Michel Roquejoffre, Lenya Ryzhik
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引用次数: 0

摘要

卢卡斯-莫尔体系是一个平均场博弈模型,通过知识的扩散来描述经济的增长。经济中的个体通过相互学习和内部创新来提高知识水平。他们的累积分布函数满足一个时间向前的非线性非局部反应-扩散型方程。另一方面,代理人的学习策略基于一个后向非局部哈密尔顿-雅各比-贝尔曼方程的解,该方程与上述代理人密度方程耦合。这些方程共同构成了一个主题领域博弈类型的系统。当学习率足够大时,卢卡斯-莫尔系统的平衡增长路径解的存在性在~/cite{PRV,Porretta-Rossi}中得到了证明。在此,我们分析了不存在平衡增长路径的互补机制。主要结果是一个长时间收敛定理。也就是说,初始-终值问题的解的表现是,在大段时间内,绝大多数代理人根本没有时间生产,而只是在学习。特别是,代理密度会以费舍尔-KPP 的速度增长。我们将这类解决方案命名为抽签社会。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Diffusion of knowledge and the lottery society
The Lucas-Moll system is a mean-field game type model describing the growth of an economy by means of diffusion of knowledge. The individual agents in the economy advance their knowledge by learning from each other and via internal innovation. Their cumulative distribution function satisfies a forward in time nonlinear non-local reaction-diffusion type equation. On the other hand, the learning strategy of the agents is based on the solution to a backward in time nonlocal Hamilton-Jacobi-Bellman equation that is coupled to the aforementioned equation for the agents density. Together, these equations form a system of the mean-field game type. When the learning rate is sufficiently large, existence of balanced growth path solutions to the Lucas-Moll system was proved in~\cite{PRV,Porretta-Rossi}. Here, we analyze a complementary regime where the balanced growth paths do not exist. The main result is a long time convergence theorem. Namely, the solution to the initial-terminal value problem behaves in such a way that at large times an overwhelming majority of the agents spend no time producing at all and are only learning. In particular, the agents density propagates at the Fisher-KPP speed. We name this type of solutions a lottery society.
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