具有联盟结构的动态对策(英文)

Dynamic Games with Coalitional Structures

现代对策论中原则上所考虑的理想对策模型可分为两类 :策略对策和合作对策。在策略对策中局中人选择使他自己获得最大支付的策略 ,在合作对策中局中人只考虑使他们所在的联盟所得支付最大 ,而联盟中个人之间如何分配并没有考虑。许多论文已经探讨了这样的问题 :当不完全合作时 ,局中人往往选择使他们所在联盟得到支付最大的策略来形成联盟。本文中考虑了具有完全信息的对策 ,并且在对策树的一些固定结点处随机地改变联盟分割 ,从而形成了构造最优子树 (分枝 )的算法 ,针对这样的对策同时也得到了一种新值 (PMS 值 )。

Game-theoretic models considered in the modern game theory in principal can be divided into two classes: strategic and cooperative games. In strategic games the players choosing their strategies try to get maximal payoffs, in cooperative games it is assumed that players try to maximize the sum of their payoffs and the problem consists in the allocation of this maximal total payoff between them. There is a number of papers where the intermediate case is considered: the case when the cooperation is not full, and players form coalitions choosing strategies with the intention to maximize the payoff of the coalition to which they belong. This paper considers games with perfect information and randomly changing coalitional partitions in some fixed vertices of the game tree. An algorithm for constructing the optimal subtree (”bunch”) is proposed and the new value (the so called PMS-value) for such games introduced.