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Game-Theoretic Models of Binary Collective Behavior

Authors
  • Breer, V. V.1
  • 1 Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia , Moscow (Russia)
Type
Published Article
Journal
Automation and Remote Control
Publisher
Pleiades Publishing
Publication Date
Nov 01, 2021
Volume
82
Issue
11
Pages
1985–1995
Identifiers
DOI: 10.1134/S0005117921110138
Source
Springer Nature
Keywords
Disciplines
  • Mathematical Game Theory and Applications
License
Yellow

Abstract

Abstract We study game-theoretic models by solving algebraic equations that characterize the Nash equilibrium rather than from the viewpoint of maxima of the players’ utility functions, as is usually done. This characterization is obtained for models of binary collective behavior, in which players choose one of two possible strategies. Based on the results for the general model, game-theoretic models of conformal threshold Binary Collective Behavior (BCB) are studied, provided the team is divided into \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L$$\end{document} groups. The conditions for the existence of Nash equilibria are proved. For each Nash equilibrium, its structure is defined. The results obtained are illustrated by two examples of conformal threshold BCB when the group coincides with the whole team and when the latter is divided into two groups. It is shown that the Nash equilibria in the first and second examples are analogs of the equilibria in M. Granovetter’s and T. Schelling’s dynamic models, respectively.

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