论文标题
与紧凑的动作空间的连续时间有限状态平均现场游戏的计划问题
Planning problem for continuous-time finite state mean field game with compact action space
论文作者
论文摘要
平均现场游戏的计划问题意味着，使用终端回报的选择，试图将许多相同的理性代理的系统从给定的分布转移到最后一个分布。它可以作为平均现场游戏系统配方，仅在测量变量上具有边界条件。在论文中，我们考虑了连续的有限状态平均现场游戏，假设每个玩家的动作空间都紧凑。结果表明，即使在初始分布中可以达到最终分布，在这种情况下的计划问题也可能无法接受解决方案。此外，我们介绍了有限状态平均现场游戏的普遍解决方案的概念，该解决方案是基于代表参与者的遗憾的最小化概念。这个最小的遗憾解决方案总是存在。此外，只要后者是非空的，一组最小的遗憾解决方案是关闭计划问题的经典解决方案。
The planning problem for the mean field game implies the one tries to transfer the system of infinitely many identical rational agents from the given distribution to the final one using the choice of the terminal payoff. It can be formulated as the mean field game system with the boundary condition only on the measure variable. In the paper, we consider the continuous-time finite state mean field game assuming that the space of actions for each player is compact. It is shown that the planning problem in this case may not admit a solution even if the final distribution is reachable from the initial one. Further, we introduce the concept of generalized solution of the planning problem for the finite state mean field game based on the minimization of regret of the representative player. This minimal regret solution always exists. Additionally, the set of minimal regret solution is the closure of the set of classical solution of the planning problem provided that the latter is nonempty.
