论文标题
平均野外游戏的逆问题
Inverse problems for mean field games
论文作者
论文摘要
平均野外游戏的理论研究了代理以某种对称方式相互互动的大系统的限制行为。运行和终端成本对于代理商决定策略至关重要。但是，在实践中，它们通常以代理商的一部分或完全未知，而总成本在游戏结束时是已知的。为了解决这个具有挑战性的问题，我们建议并研究平均野外游戏的几个反问题。当Lagrangian是一种动能时，我们首先建立唯一的可识别性结果，这表明人们可以从了解总成本的知识中恢复运行成本或终端成本。如果运行成本仅限于与时间无关的类别，我们可以进一步证明人们可以同时恢复运行和终端成本。最后，我们将结果扩展到了拉格朗日将军。
The theory of mean field games studies the limiting behaviors of large systems where the agents interact with each other in a certain symmetric way. The running and terminal costs are critical for the agents to decide the strategies. However, in practice they are often partially known or totally unknown for the agents, while the total cost is known at the end of the game. To address this challenging issue, we propose and study several inverse problems for mean field games. When the Lagrangian is a kinetic energy, we first establish unique identifiability results, showing that one can recover either the running cost or the terminal cost from knowledge of the total cost. If the running cost is limited to the time-independent class, we can further prove that one can simultaneously recover both the running and the terminal costs. Finally, we extend the results to the setup with general Lagrangians.
