Diffusion control games with rank-based rewards

具有基于等级的奖励的扩散控制游戏

• 批准号: 448228684
• 负责人: Professor Dr. Stefan Ankirchner
• 金额: --
• 依托单位: Lehrstuhl für Stochastische Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/448228684?language=en
• 关键词: Diffusion; control; games; rank; based

The general aim of the project is to understand the impact of interaction and rank-based rewards on how economic agents choose diffusion controls, and to provide methods for computing and approximating Nash equilibria. More specifically, we plan to analyze stochastic differential games, where each player can choose the diffusion intensity of her state process. The diffusion intensity control of each player is assumed to take values in a fixed bounded interval and to be progressively measurable with respect to a filtration representing the player's information flow. Moreover, we assume that the reward of each player depends on the rank of her state process at a given finite time horizon. In the first part we aim at analyzing a stylized zero-sum 2-player game, where each of the two players strives to maximize the probability of being ahead of the opponent. Besides, each of the player's state is assumed to be a Brownian martingale. Our first aim is to provide sufficient and necessary conditions of Nash equilibria in pure Markov controls to exist. Moreover, the effect of common noise in both players' states will be carved out. Finally, we aim at investigating some generalizations, e.g. by allowing for mixed strategies and non-symmetric control sets. The second part is devoted to an analysis of diffusion control games with more than two players. For some specific rank-based rewards we aim at determining a Nash equilibrium explicitly. The discontinuity of rank-based reward, however, make the n-player case difficult to analyze in general. Therefore, the project will contribute towards opening mean field techniques for approximating Nash equilibria in diffusion control games with rank-based rewards. To this end, we will consider mean field control problems, the solution of which approximate, for large n, equilibrium strategies of n-player diffusion control games.

该项目的总体目标是了解相互作用和基于排名的报酬对经济主体如何选择扩散控制的影响，并提供计算和近似纳什均衡的方法。更具体地说，我们计划分析随机微分对策，其中每个参与者可以选择其状态过程的扩散强度。假设每个玩家的扩散强度控制在固定的有界区间中取值，并且相对于表示玩家信息流的过滤是渐进可测量的。此外，我们假设每个参与者的报酬取决于她的状态过程在给定的有限时间范围内的等级。在第一部分中，我们旨在分析一个程式化的零和两人博弈，其中两个参与者都努力最大化领先于对手的可能性。此外，假设博弈者的每一个状态都是一个布朗鞅。我们的第一个目标是给出纯马氏控制中纳什均衡存在的充要条件。此外，两个玩家状态下的共同噪音的影响也将被剔除。最后，我们的目的是研究一些推广，例如，允许混合策略和非对称控制集。第二部分分析了具有两个以上参与者的扩散控制博弈。对于某些特定的基于等级的报酬，我们的目标是明确地确定一个纳什均衡。然而，基于排名的奖励的不连续性使得n人案例很难从总体上分析。因此，该项目将有助于开放平均场技术，以近似扩散控制博弈中的纳什均衡与排名为基础的奖励。为此，我们将考虑平均场控制问题，其解对于大n，近似于n人扩散控制对策的均衡策略。