一种求解合作博弈最公平核心的非精确平行分裂算法

A kind of inexact parallel splitting method for solving the fairest core in cooperative game

针对合作博弈核心和Shapley值的特点,将最公平核心问题转化为带有两个变量的可分离凸优化问题,引入结构变分不等式的算子分裂方法框架,提出了求解最公平核心的一种非精确平行分裂算法.而且,该算法充分利用了所求解问题的可行域的简单闭凸性,子问题的非精确求解是容易的.最后,简单算例的数值实验表明了算法的收敛性和有效性.

In this paper, considering the characteristics of the core and the Shapley value in cooperative game, we transform the fairest core problem into a separable convex optimization problem with two variable. A kind of inexact parallel splitting method is proposed for solving the fairest core by introducing the operator splitting method framework of structured variational inequalities. Furthermore, the proposed method makes full use of the simple closed convexity of the feasible region in the solved problem, and all sub-problems are easy to be solved inexactly. Finally, some numerical results of a simple example indicate the convergence and validity of this method.