2003 Fiscal Year Final Research Report Summary

A Mathematical Analysis on the Conditions of Solidarity

Research Project

Project/Area Number	14510244
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	社会学(含社会福祉関係)
Research Institution	Fukuoka University
Principal Investigator	KOBAYASHI Junichi Fukuoka University, Faculty of Humanities, Professor, 人文学部, 教授 (20113243)
Project Period (FY)	2002 – 2003
Keywords	evolutionary games / social order / ESS / solidarity / fictitious play
Research Abstract	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.