The pairwise comparison dynamic is a forward ordinary differential equation in a Banach space whose solution is a time-dependent probability measure to maximize utility based on a nonlinear and nonlocal protocol. It contains a wide class of evolutionary game models, such as replicator dynamics and its generalization. We present an inverse control approach to obtain a replicator-type pairwise comparison dynamic from the large discount limit of a mean field game (MFG) as a coupled forward-backward system. This methodology provides a new interpretation of replicator-type dynamics as a myopic perception limit of the dynamic programming. The cost function in the MFG is explicitly obtained to derive the generalized replicator dynamics. We present a finite difference method to compute these models such that the conservation and nonnegativity of the probability density and bounds of the value function can be numerically satisfied. We conduct a computational convergence study of a large discount limit, focusing on potential games and an energy management problem under several conditions.
A DEMATEL-Based Completion Method for Incomplete Pairwise Comparison Matrix in AHP
Southwest University（西南大学）；Jinan University（暨南大学）；Vanderbilt University（范德堡大学）；The Hong Kong Polytechnic University（香港理工大学）；University of Portsmouth（朴茨茅斯大学）
Refined thresholds for inconsistency: The effect of the graph associated with incomplete pairwise comparisons
Corvinus University of Budapest (BCE), Institute of Operations and Decision Sciences, Department of Operations Research and Actuarial Sciences（布达佩斯考文纽斯大学）；Institute for Computer Science and Control (SZTAKI), Hungarian Research Network (HUN-REN)（匈牙利国家研究网络计算机科学与控制研究所）
Size independence of consistency index for pairwise comparison matrices in analytic hierarchy process
Faculty of Science and Engineering, Otemon Gakuin University（帝塚山学院大学理工学部）；Faculty of Applied Information Science, Hiroshima Institute of Technology（广岛工业大学应用信息科学部）
Inconsistency thresholds for incomplete pairwise comparison matrices
Corvinus University of Budapest (BCE)（布达佩斯考文纽斯大学）；Institute for Computer Science and Control (SZTAKI)（计算机科学与控制研究所）；Eötvös Loránd Research Network (ELKH)（厄特沃什·罗兰研究网络）
The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices
GNNRank: Learning Global Rankings from Pairwise Comparisons via Directed Graph Neural Networks
University of Oxford（牛津大学）；Amazon Web Services AI Shanghai Lablet（亚马逊云科技AI上海实验室）；The Alan Turing Institute（阿兰·图灵研究所）；Shanghai Jiao Tong University（上海交通大学）；Shanghai AI Laboratory（上海人工智能实验室）
