Abstract In multi-agent decision making, agents’ decisions are coherently interdependent, and the objectives of agents are possibly inconsistent. In this type of decision-making, agents need to reason and act strategically. Therefore, game theory can be used to study the strategic interactions among decision-makers. This paper presents a new hierarchical decision-making methodology, which uses the advantages of both game theory (i.e. Stackelberg leadership model) and Evidential Reasoning (ER). ER, as a multi-attribute decision-making method, considers both qualitative and quantitative attributes, and incorporates existing uncertainties in evaluating alternatives. The backward induction method and Monte-Carlo theory are used to solve the deterministic and stochastic forms of the proposed leader–follower game. The methodology is applied to choose the best restoration scenario for Urmia Lake, which is the biggest saltwater lake in the Middle East. In the past decade, the lake’s surface area has dramatically decreased due to climate change and an anthropogenic drought. In this paper, 19 lake restoration scenarios have been evaluated, and a scenario, which is corresponding to a 40% reduction in agricultural water consumption and water release from Nezam Abad dam, is found to be the equilibrium solution for both types of the game.

中文翻译：

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不确定性下分层多智能体决策的基于证据推理的领导者-跟随者博弈

摘要 在多智能体决策中，智能体的决策相互依存，智能体的目标可能不一致。在这种类型的决策中，代理需要进行推理和战略性行动。因此，博弈论可以用来研究决策者之间的战略互动。本文提出了一种新的分层决策方法，它利用了博弈论（即 Stackelberg 领导模型）和证据推理（ER）的优点。ER作为一种多属性决策方法，同时考虑定性和定量属性，并在评估备选方案时结合现有的不确定性。反向归纳法和蒙特卡洛理论被用来解决所提出的领导者 - 追随者博弈的确定性和随机形式。应用该方法为中东最大的咸水湖乌尔米亚湖选择最佳修复方案。在过去十年中，由于气候变化和人为干旱，该湖的表面积急剧减少。本文评估了 19 个湖泊修复方案，发现一个对应于农业用水量和 Nezam Abad 大坝放水量减少 40% 的方案是两种博弈的均衡解。