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.

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