多目标动态优化中Pareto随机合作博弈研究综述

随着经济全球化的不断深入,“合作共赢”的发展战略越来越被人们接受,进而合作博弈也被合理地应用到多个领域.与静态合作博弈相比,动态博弈的约束条件为动态方程,其具有优化行为、多个玩家共同存在、决策结果的持久性以及对环境变化的鲁棒性等特点.由于动态系统总是受到某些随机波动的干扰,将这些内部随机波动和外部随机扰动考虑到系统模型中更为实际.随机动态合作博弈同时考虑策略行为、动态演化与随机因素之间的相互作用,其可能是最复杂的决策形式之一.鉴于此,对多目标动态优化中随机合作博弈的进展进行综述:首先,回顾多目标合作博弈的研究背景,给出Pareto最优性的定义和基本性质;其次,综述确定性的合作博弈;再次,分别论述随机合作博弈和平均场随机合作博弈;最后,提出随机合作博弈几个未来研究方向.

Pareto stochastic cooperative games in multiobjective dynamic optimization problems: A survey

With the deepening of economic globalization, the concept of win-win cooperation is more and more accepted by people and the cooperative game is applied appropriately to various fields. Compared with the static cooperative game, the dynamic game is subject to dynamic systems, which possess the features of optimizing actions, the co-existence of multiple players, and enduring consequences of decisions and robustness with regard to variability in the environment. Because the dynamic system is always disturbed by some random perturbations, it is natural to consider these internal random perturbations and external random disturbances in the dynamic model. The stochastic dynamic cooperative game may be one of the most complex decision-making forms, as it considers the interaction among strategic behavior, dynamic evolution and stochastic factors. Based on the above discussions, we generalize the progress of the stochastic cooperative game in the multiobjective dynamic optimization: Firstly, the research background of the cooperative game in the multiobjective optimization problem is reviewed, and the definition and fundamental properties of Pareto optimality are presented; secondly, the deterministic cooperative game is summarized; moreover, the stochastic cooperative game and the mean-field stochastic cooperative game are summarized; finally, several future research directions of the stochastic cooperative game are proposed.