随机自适应动态博弈

Stochastic adaptive dynamical games

在不确定性结构和环境下的动态博弈是重要的复杂系统问题,然而现有文献少有理论研究.本文将博弈论思想与自适应控制方法相结合,考虑系数未知的线性随机系统在输出跟踪二次型指标下,两人零和自适应博弈问题.具体来讲,先用最小二乘算法对未知参数进行在线估计,再根据"必然等价原则"设计博弈策略组合.本文在随机适应控制理论基础上,证明了相应闭环博弈系统是全局稳定的,并且行动组合在一定意义下是博弈问题的渐近Nash均衡解.

In this paper, we consider two players zero-sum dynamical games in linear stochastic systems described by input-output model with unknown parameters, and with an ergodic output-tracking quadratic index. We combine the ideas of game theory and control theory as a modeling method, and investigate the corresponding stochastic adaptive game problems. There is few existing results related to such stochastic adaptive game problems, since uncertainty raises the difficulty of making decisions for both players. We attempt to cope with this problem by the ideas and methods of adaptive control. We will firstly use the standard least squares to estimate the unknown parameters, and then construct the adaptive strategy profile for both players by using the so-called ＂certainty equivalence principle＂. We will prove that, the adaptive strategic profile makes the system globally stable, and that the action profile is an asymptotic Nash equilibrium solution to our game problem in a certain sense.