摘要
提出一种基于M ealy自动机的博弈模型,并应用于二人重复囚徒困境博弈。采用M ealy自动机对博弈参与人的决策行为进行建模,在模型中每个博弈参与人选择一个有限自动机,有限自动机在当前状态下与竞争对手的有限自动机进行博弈,依据所获取的效用转换到下一状态,并开始新一周期的博弈。在博弈过程中参与人追求平均效用最大,同时决策复杂度最小,这里用有限自动机的状态个数表示决策复杂度,模型解是一对有限自动机,有限自动机对在每阶段博弈中都是最优的。采用M ealy自动机表示单一战略、针锋相对战略、冷酷战略和带有惩罚的战略等几种常见的重复囚徒困境博弈战略模型,定义了基于M ealy自动机的重复博弈平均效用、纳什均衡、精炼均衡等概念,给出了定义的相关性质,并对这些性质进行证明。
The repeated games model based on Mealy automaton is presented and applied to study two-person repeated game the player＇s decision-making model is constructed by Mealy automaton and the player chooses a Mealy automaton in model. The player＇s automaton at current state is gaming with other＇s automaton. The player＇s automaton moves into the next state according to the payoff acquired in the game. A new game is started at the new state. A player＇s aim is to maximize his average payoff and subject to that, to minimize complexity in the process of game, The measure of complexity is the number of automaton＇s states. A solution is defined as a pair of automaton in which the choice of machine is optimal for each player at every stage of the game. Several common repeated prisoner＇s dilemma game is constructed, such as plays 1 constantly strategy, tit-for-tat strategy, grim strategy and strategy with punishment. The definitions of repeated game theory based on Mealy automata, such as the payoff of repeated game, Nash equilibrium and perfect equilibrium base on Mealy are showed. The properties of these definitions are given and demonstrated,
出处
《管理科学》
CSSCI
2006年第5期66-70,共5页
Journal of Management Science
基金
国家自然科学基金(90510016)
