Skip to main content
SpringerLink
Log in

Game-Theoretic Models of Binary Collective Behavior

  • MATHEMATICAL GAME THEORY AND APPLICATIONS
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

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 \(L\) 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Conformity in social psychology is a change in the behavior of an individual that occurs as a result of real or perceived influence from other people [8].

  2. In Example 3.1 there are no “foe” groups; in Example 3.2 there is one “foe” group.

  3. What exactly the choice of zero or one means is a matter of agreement in a particular application. For example, \(\omega _{li}=1 \) in Example 3.1 means participation in the riots and in Example 3.2 it is living in the area of interest.

REFERENCES

  1. Breer, V.V., Game-theoretic models of collective conformity behavior, Autom. Remote Control, 2012, no. 10, pp. 111–126.

  2. Breer, V., V., and Novikov, D.A., Threshold models of mutual insurance, Autom. Remote Control, 2015, vol. 76, pp. 897–908.

    Article  MathSciNet  Google Scholar 

  3. Gubko, M.V. and Novikov, D.A., Teoriya igr v upravlenii organizatsionnymi sistemami (Game Theory in the Control of Organizational Systems), Moscow: Sinteg, 2002.

    Google Scholar 

  4. Malishevskii, A.V., Kachestvennye modeli v teorii slozhnykh sistem (Qualitative Models in the Theory of Complex Systems), Moscow: Fizmatlit, 1998.

    Google Scholar 

  5. Mazalov, V.V., Matematicheskaya teoriya igr i ee prilozheniya (Mathematical Game Theory and Applications), St. Petersburg: Lan’, 2017.

    Google Scholar 

  6. Opoitsev, V.I., Ravnovesie i ustoichivost’ v modelyakh kollektivnogo povedeniya (Equilibrium and Stability in Collective Behavior Models), Moscow: Nauka, 1977.

    Google Scholar 

  7. Akhmetzhanov, A.R., Worden, L., and Dushoff, J., Effects of mixing in threshold models of social behavior, Phys. Rev. E. Stat. Nonlinear Soft Matter Phys., 2013, vol. 88 (1), p. 012816.

    Article  Google Scholar 

  8. Aronson, E., Wilson, T.D., Akert, M.R., and Sommers, S., Social Psychology, Pearson–Prentice Hall, 2016.

  9. Axelrod, R. and Tesfatsion, L., Guide for newcomers to agent-based modeling in the social sciences, in Handbook of Computational Economics, 2006, vol. 2, pp. 1648–1659.

  10. Barra, A. and Agliari, E., A statistical mechanics approach to Granovetter theory, Physica A: Stat. Mech. Appl., 2012, vol. 391 (10), pp. 3017–3026.

    Article  Google Scholar 

  11. Coleman, J.S., Foundations of Social Theory, Harvard: Harvard Univ. Press, 1994.

    Google Scholar 

  12. Granovetter, M., Threshold models of collective behavior, Am. J. Sociol., 1978, vol. 83 (6), pp. 1420–1443.

    Article  Google Scholar 

  13. Schelling, T.C., Micromotives and Macrobehavior, New York–London: W.W. Norton, 2006.

    Google Scholar 

  14. Zhang, J., Tipping and residential segregation: a unified Schelling model, J. Reg. Sci., 2011, vol. 51 (1), pp. 167–193.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    V. V. Breer

Authors
  1. V. V. Breer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Breer.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Breer, V.V. Game-Theoretic Models of Binary Collective Behavior. Autom Remote Control 82, 1985–1995 (2021). https://doi.org/10.1134/S0005117921110138

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117921110138

Keywords

Search

Navigation