title: Local Nash equilibrium in social networks.
abstract: Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before they adopt a unified strategy. In this scenario, a new strategy equilibrium emerges in the system. We define this equilibrium as a local Nash equilibrium. In this paper, we present an explicit definition of the local Nash equilibrium for the two-strategy games in structured populations. Based on the definition, we investigate the condition that a system reaches the evolutionary stable state when the individuals play the Prisoner's dilemma and snow-drift game. The local Nash equilibrium provides a way to judge whether a gaming structured population reaches the evolutionary stable state on one hand. On the other hand, it can be used to predict whether cooperators can survive in a system long before the system reaches its evolutionary stable state for the Prisoner's dilemma game. Our work therefore provides a theoretical framework for understanding the evolutionary stable state in the gaming populations with static structures.
authors.affiliation: 1] Normandie Univ, France; ULH, LMAH, F-76600 Le Havre; FR-CNRS-3335, ISCN, 25 rue Ph. Lebon, 76600 Le Havre, France [2] Department of Computer Science and Technology, Tongji University, 4800 Cao'an Road, Shanghai 201804, China.
authors.forename: Yichao
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Normandie Univ, France; ULH, LMAH, F-76600 Le Havre; FR-CNRS-3335, ISCN, 25 rue Ph. Lebon, 76600 Le Havre, France.
authors.forename: M A
authors.initials: MA
authors.lastname: Aziz-Alaoui
authors.affiliation: Normandie Univ, France; ULH, LITIS, F-76600 Le Havre; FR-CNRS-3638, ISCN, 25 rue Ph. Lebon, 76600 Le Havre, France.
authors.forename: Cyrille
authors.initials: C
authors.lastname: Bertelle
authors.affiliation: Department of Computer Science and Technology, Tongji University, 4800 Cao'an Road, Shanghai 201804, China.
authors.forename: Jihong
authors.initials: J
authors.lastname: Guan
mesh_terms: D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D007398:Interpersonal Relations; D015233:Models, Statistical; D060756:Social Networking