A Mathematical Analysis on the Conditions of Solidarity

在本研究中，我们着眼于进化博弈理论，以构建一个关于团结条件的数学模型。我们试图用梅纳德-史密斯式的进化模型的思想来接近霍布斯的问题秩序。我们强调在具有“自我识别策略”的博弈中自发秩序的可能性。接下来，我们关注Young作为适应性学习模型的“虚拟游戏”。杨氏模型被表述为（高阶）马尔可夫链。我们继续关注“摄动”马尔可夫链模型。在这个模型中，随机稳定性的概念是很重要的。我们将这一概念应用到Fararo=Skvoretz的优势关系网络模型中，并阐明了该模型中的层次类型是随机稳定状态。

In this study, we focus on the theory of evolutionary games in order to construct a mathematical model about the conditions of solidarity. We attempt to approach the Hobbesian problem order using the ideas of evolutionary model of Maynard-Smith type. We emphasize the possibility of spontaneous order in the case of the game with"self-recognizing strategies."Next we pay attention on the "fictitious play" as a model of adaptive learning by Young. Young's model is formulated as the (higher order) Markov chain. And we proceed to focus on the "perturbed" Markov chain model. In this model, the concept of the stochastic stability is important. We apply this concept to the model on the networks of dominance relationships by Fararo=Skvoretz and clarify the hierarchy type is the stochastic stable state in the model.