知识增长Boltzmann平均场对策模型的平衡增长路径解
Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth
摘要：
本文研究了Lucas等人[13]提出的玻尔兹曼平均场对策模型的平衡增长路径解。代理可以通过在学习活动中交换想法来提高他们的知识水平，或者通过使用他们已经拥有的知识来生产商品。平衡增长路径解的存在意味着总产量随时间的指数增长性。当个体关于其知识水平的初始分布满足Pareto尾条件时，证明了平衡增长路径解的存在性.此外，我们给出了第一个洞察到这样的解决方案的存在性，如果除了生产和知识交流的知识水平的几何布朗运动演变。
英文摘要：
In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas et al [13] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We proof existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
