A Mathematical Analysis on the Conditions of Solidarity

点击翻译按钮获取中文摘要

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.