Econ Papers Daily / 期刊论文
期望收益连续性的一个简单证明
A simple proof of the continuity of expected payoffs
摘要
In n -person games with compact strategy spaces and continuous payoff functions, the expected payoff functions of the mixed extension are continuous with respect to the product of the weak topologies. We provide an elementary proof of this fact. The analysis reveals that the Hausdorff separation axiom, commonly imposed on the topology of players’ strategy spaces, is not needed. We also show that the definition of expected payoffs as an iterated integral does not depend on the ordering of the players.
中文摘要
在具有紧策略空间和连续支付函数的n人博弈中，混合扩展的期望支付函数关于弱拓扑的乘积是连续的。我们给出了这一事实的初等证明。分析表明，通常施加于参与者策略空间拓扑的豪斯多夫分离公理并非必要。我们还证明了将期望支付定义为迭代积分的结果不依赖于参与者的顺序。