Advertisement

An Example of Reflexive Analysis of a Game in Normal Form

  • Denis Fedyanin
Chapter
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)

Abstract

In this paper we considered a normal form game with a parameter A and suggested that this is an uncertain parameter for agents and they have to make some suggestion about it. We took a normal form game and weakened a suggestion on common knowledge. We introduced two fundamental alternatives based on dynamic epistemic logic and found equilibria for this modified game. We used the special property of these alternatives which let us calculate an equilibria by solving several normal form games with perfect information. We found direct expressions for equilibria for nonmodified game and for modified games with alternative suggestions on beliefs.

Keywords

Social networks Epistemic models Control Uncertainty Information control Game theory Collective actions de Groot’s model Logic models 

Notes

Acknowledgements

The article was prepared within the framework of the HSE University Basic Research Program and funded by the Russian Academic Excellence Project ’5-100.

References

  1. 1.
    Aumann, R.J.: Interactive epistemology I: knowledge. Int. J. Game Theory 28(3), 263–300 (1999)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Novikov, D., Chkhartishvili, A.: Reflexion Control: Mathematical Models. Communications in Cybernetics, Systems Science and Engineering (Book 5). CRC Press, Boca Raton (2014)Google Scholar
  3. 3.
    Fedyanin, D.: Threshold and network generalizations of muddy faces puzzle. In: Proceedings of the 11th IEEE International Conference on Application of Information and Communication Technologies (AICT2017, Moscow) vol. 1, pp. 256–260 (2017)Google Scholar
  4. 4.
    Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, New York (2008)CrossRefGoogle Scholar
  5. 5.
    Harsanyi, J.C.: Games with incomplete information played by Bayesian players, part I. Manag. Sci. 14(3), 159–183 (1967)CrossRefGoogle Scholar
  6. 6.
    Harsanyi, J.C.: Games with incomplete information played by Bayesian players, part II. Manag. Sci. 14(5), 320–334 (1967)CrossRefGoogle Scholar
  7. 7.
    Harsanyi, J.C.: Games with incomplete information played by Bayesian players, part III. Manag. Sci. 14(7), 486–502 (1968)CrossRefGoogle Scholar
  8. 8.
    Fedyanin, D.N., Chkhartishvili, A.G.: On a model of informational control in social networks. Autom. Remote. Control 72, 2181–2187 (2011)CrossRefGoogle Scholar
  9. 9.
    Cournot, A.: Reserches sur les Principles Mathematiques de la Theorie des Richesses. Hachette, Paris. Translated as Research into the Mathematical Principles of the Theory of Wealth. Kelley, New York (1960)zbMATHGoogle Scholar
  10. 10.
    Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83, 489–515 (1978)Google Scholar
  11. 11.
    Breer, V.V., Novikov, D.A., Rogatkin, A.D.: Mob Control: Models of Threshold Collective Behavior. Studies in Systems, Decision and Control. Springer, Heidelberg (2017)CrossRefGoogle Scholar
  12. 12.
    Sarwate, A.D., Javidi, T.: Distributed learning from social sampling. In: 46th Annual Conference on Information Sciences and Systems (CISS), Princeton, 21–23 March 2012, pp. 1–6. IEEE, Piscataway (2012)Google Scholar
  13. 13.
    DeGroot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 69, 118–121 (1974)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Denis Fedyanin
    • 1
    • 2
    • 3
  1. 1.V.A. Trapeznikov Institute of Control SciencesMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.IEEEMoscowRussia

Personalised recommendations