论文标题
吸收有限域中的主方程
The Master Equation in a Bounded Domain with Absorption
论文作者
论文摘要
我们在平均野外游戏理论中分析了主方程和收敛问题，考虑到具有均匀条件的有限域。该框架表征了n-players差异游戏，在触摸边界时，每个玩家的动态结束，导致主方程中的两个Dirichlet边界条件。在本文的第一部分中，我们分析了主方程的适当性及其解决方案的规律性，以研究适用类抛物线方程的解决方案边界处的全球规律性。然后利用此类结果来考虑NASH均衡的收敛问题，即N-players系统中的平均现场游戏系统策略，也证明了最佳轨迹收敛。最终，我们应用发现来解决与最佳清算方案有关的玩具模型。
We analyze the Master Equation and the convergence problem within Mean Field Games theory considering a bounded domain with homogeneous Dirichlet conditions. This framework characterizes N-players differential games where each player's dynamic ends when touching the boundary, leading to two Dirichlet boundary conditions in the Master Equation. In the first part of the paper we analyze both the well-posedness of the Master Equation and the regularity of its solutions studying the global regularity at the boundary of solutions for a suitable class of parabolic equations. Such results are then exploited to consider the convergence problem of the Nash equilibria, towards the Mean Field Games system strategies, in the N-players system, also proving optimal trajectories convergence. Eventually, we apply our findings to solve a toy model related to an optimal liquidation scenario.
