Microscopic Foundation of Stochastic Game Dynamical Equations
Microscopic Foundation of Stochastic Game Dynamical Equations
复制标题
DOI：
10.1007/978-94-017-1654-3_18
复制
发表时间：
1998-05
期刊：
影响因子：
--
通讯作者：
D. Helbing
中科院分区：
文献类型：
--
作者：
D. Helbing
自从冯·诺伊曼和摩根斯坦开创了博弈论领域以来，博弈论经常被证明对个体之间的竞争与合作的定量描述和理解具有很大的价值。博弈论主要关注两个问题：1。在给定情况下，哪种策略是最优策略？2. 在个体反复互动的情况下，策略选择的动态是什么？在这方面，博弈论动力学方程得到了越来越多的关注。尽管它们与进化理论的复制因子方程一致（参见第二节），但它们不能以同样的方式被证明是合理的。因此，我们将寻找基于个体行动和决策的游戏动力学方程的基础（参见第4节）。此外，我们将制定进化博弈论的随机版本（参见第三节）。这使我们能够研究波动对社会系统动态的影响。为了说明基本思想，提出了行为约定自组织的具体模型（参见第五节）。我们将看到，博弈动力学方程只能描述有限时间内社会系统的平均进化。因此，将制订其有效性的标准（参见第六节）。最后，我们将提出对更一般行为模型的可能扩展，并讨论博弈动力学方程的实际含义（参见第七节）。
Since von Neumann and Morgenstern initiated the field of game theory, l it has often proved of great value for the quantitative description and understanding of competition and co-operation between individuals. Game theory focusses on two questions: 1. Which is the optimal strategy in a given situation? 2. What is the dynamics of strategy choices in cases of repeatedly interacting individuals? In this connection game dynamical equations2 find a steadily increasing interest. Although they agree with the replicator equations of evolution theory (cf. Sec. II), they cannot be justified in the same way. Therefore, we will be looking for a foundation of the game dynamical equations which is based on individual actions and decisions (cf. Sec. IV).In addition, we will formulate a stochastic version of evolutionary game theory (cf. Sec. III). This allows us to investigate the effects of fluctuations on the dynamics of social systems. In order to i1lustrate the essential ideas, a concrete model for the self-organization of behavioral conventions is presented (cf. Sec. V). We will see that the game dynamical equations describe the average evolution of social systems only for restricted time periods. Therefore, a criterium for their validity will be developed (cf. Sec. VI). Finally, we will present possible extensions to more general behavioral models and discuss the actual meaning of the game dynamical equations (cf. Sec. VII).