论文标题
委托人与代理领域之间的基于等级的奖励：申请节省能源
A Rank-Based Reward between a Principal and a Field of Agents: Application to Energy Savings
论文作者
论文摘要
在本文中，我们考虑了旨在为异构代理人设计奖励功能的主要问题的问题。我们根据代理的排名来构建一种激励措施，以便开始后者之间的竞争。我们将自己置于平均场类型相互作用的极限设置中，并证明给定奖励的平衡分布的存在和唯一性，我们可以找到明确的表示。首先专注于同质环境，我们使用问题的凸重新印象来表征最佳的奖励函数，并提供对其行为的解释。然后，我们证明这种特征仍然适用于一类异质种群。对于一般情况，我们提出了一种收敛的数值方法，该方法充分利用了平均场平衡的表征。我们根据使用现实数据的使用制定了与法国节能证书市场有关的案例研究，这表明排名系统允许实现欧洲委员会实施的清醒目标。
In this paper, we consider the problem of a Principal aiming at designing a reward function for a population of heterogeneous agents. We construct an incentive based on the ranking of the agents, so that a competition among the latter is initiated. We place ourselves in the limit setting of mean-field type interactions and prove the existence and uniqueness of the equilibrium distribution for a given reward, for which we can find an explicit representation. Focusing first on the homogeneous setting, we characterize the optimal reward function using a convex reformulation of the problem and provide an interpretation of its behaviour. We then show that this characterization still holds for a sub-class of heterogeneous populations. For the general case, we propose a convergent numerical method which fully exploits the characterization of the mean-field equilibrium. We develop a case study related to the French market of Energy Saving Certificates based on the use of realistic data, which shows that the ranking system allows to achieve the sobriety target imposed by the European commission.
