论文标题
未知竞赛的finetti问题
The de Finetti problem with unknown competition
论文作者
论文摘要
我们考虑了一个资源提取问题，该问题扩展了经典的finetti问题，以便在维纳过程中包括一个案例，当时竞争对手可能存在一个可能存在的所有剩余资源的竞争对手；我们将这种未知的竞争解释为受到可能欺诈的代理人。这种情况被建模为具有不完整信息的控制器和静止的非零和随机游戏。为了允许欺诈者掩盖他的存在，我们考虑了他的行动时间随机的策略。在这些条件下，我们提供了NASH均衡，该平衡是根据相应的单人finetti问题进行了充分描述的。在这种均衡中，代理和欺诈者使用奇异策略的方式，即代表可用资源的二维过程和主动竞争的过滤估计，反映了沿特定边界的特定方向。
We consider a resource extraction problem which extends the classical de Finetti problem for a Wiener process to include the case when a competitor, who is equipped with the possibility to extract all the remaining resources in one piece, may exist; we interpret this unknown competition as the agent being subject to possible fraud. This situation is modelled as a controller-and-stopper non-zero-sum stochastic game with incomplete information. In order to allow the fraudster to hide his existence, we consider strategies where his action time is randomised. Under these conditions, we provide a Nash equilibrium which is fully described in terms of the corresponding single-player de Finetti problem. In this equilibrium, the agent and the fraudster use singular strategies in such a way that a two-dimensional process, which represents available resources and the filtering estimate of active competition, reflects in a specific direction along a given boundary.
