Nash Equilibrium Strategies in Extensive Form Games and Sub Games

Authors

  • Karthi C. Research Scholar, Department of Mathematics. Author
  • Selvakumari K. Professor, Department of Mathematics, Vels Institute of Science, Technology and Advanced Studies, Chennai, Tamilnadu, India Author

DOI:

https://doi.org/10.61841/gszj8k05

Keywords:

Nash Equilibrium Strategies Pure Strategy, Mixed Strategy, Extensive Form Games, Sub Games

Abstract

Nash Equilibrium solutions are a common solution concept of extensive form games in two-player zero-sum games and bimatrix games. It determines the analysis of subgame-perfect pure and mixed strategy equilibria and the sequential equilibria concept. The main aim of the paper is to investigate the pure and mixed Nash equilibrium strategies of two-person zero-sum games with extensive form games and subgames and provide tools for its systematic study. 

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References

[1] Dresher M (1961). The Mathematics of Games of Strategy. Theory & applications (Ch 4: Games in Extensive form, PP. 74-78) Rand Corp ISBN 0-486-64216

[2] J. Kuipers, J. Flesch, G. Schoenmakers, K. Vrieze, 2009, European Journal of Operational Research, Pure subgame – Perfect Equilibria in Free Transition Games.

[3] Refinement of the Nash equilibrium concept by E. Van Damme.

[4] K G Binmore, 1985, Equilibria in Extensive form games The Economic Journal 95 (supplement), 51-59.

[5] Kuhn H 1950 Extensive games, Proceedings of the National Academy of Sciences of the United States of America 36, 570-6

[6] Kuhn H 1953 Extensive games the Problem of information In Contributions to the Theory of Games, Volume II (Annals of Mathematics studies 28) Ed. H Kuhn & A Tucker, Princeton

[7] Kimmo Berg, Gijs Schoenmakers 2017, Construction of Subgame – Perfect Mixed Strategy Equilibria in Repeated games 8 (4), 47

[8] Nash JF (1951), Non-cooperative game, Ann of Math, Vol 54, PP 286-295.

[9] Philip J Reny, 1992, The Journal of Economic Perspectives Rationality in Extensive form games, Vol. 16, No 4,. 103-118

[10] R J Aumann, Game Theory

[11] Reny P 1999 on the existence of pure & mixed strategy Nash equilibrium in discontinuous games. Econometrica 67, 1029-56

[12] Robert Stalmaker, 1999, Research in Economics; Extensive & Strategic forms Games & Models for Games Vol 53, Issue 3, PP. 293–319

[13] Selten, Rein (1975), Re-examination of the Perfectness Concept for Equilibrium Points in Extensive Form Games. Int. J. Game Theory, Vol. 4, pp. 25-55.

[14] Von Neumann, J. & Morgenstern, O. 1944. Theory of Games & Economic Behavior. Princeton, NJ Princeton University Press.

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Published

31.07.2020

How to Cite

C. , K., & K. , S. (2020). Nash Equilibrium Strategies in Extensive Form Games and Sub Games. International Journal of Psychosocial Rehabilitation, 24(5), 354-362. https://doi.org/10.61841/gszj8k05