A Forward-Looking Nash Game and Its Application to Achieving Pareto-Efficient Optimization

Jie Ren; Kai-Kit Wong; Jianjun Hou

doi:10.4236/am.2013.412218

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Applied Mathematics > Vol.4 No.12, December 2013

A Forward-Looking Nash Game and Its Application to Achieving Pareto-Efficient Optimization ()

Department of Electronic and Electrical Engineering, University College London, Torrington Place, London, UK.
School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing, China.

DOI: 10.4236/am.2013.412218 PDF HTML 3,346 Downloads 4,955 Views Citations

Abstract

Recognizing the fact that a player’s cognition plays a defining role in the resulting equilibrium of a game of competition, this paper provides the foundation for a Nash game with forward-looking players by presenting a formal definition of the Nash game with consideration of the players’ belief. We use a simple two-firm model to demonstrate its fundamental difference from the standard Nash and Stackelberg games. Then we show that the players’ belief functions can be regarded as the optimization parameters for directing the game towards a much more desirable equilibrium.

Keywords

Belief; Cognition; Iterative Algorithm; Nash Equilibrium; Pareto-Optimality; Stackelberg

Share and Cite:

Ren, J. , Wong, K. and Hou, J. (2013) A Forward-Looking Nash Game and Its Application to Achieving Pareto-Efficient Optimization. Applied Mathematics, 4, 1609-1615. doi: 10.4236/am.2013.412218.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. J. Osborne and A. Rubinstein, “A Course in Game Theory,” MIT Press, Cambridge, 1994.
[2]	G. H. Von Stackelberg, “Market Structure and Equilibrium,” Springer-verlag, Berlin, Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-12586-7
[3]	E. Rasmusen, “Game and Information,” Basil Backwell Ltd., Oxford, 1989.
[4]	J. Nash, “Non-Cooperative Games,” The Annals of Mathematics, Vol. 54, No. 2, 1951, pp. 286-295. http://dx.doi.org/10.2307/1969529
[5]	D. Fudenberg and J. Tirole, “Game Theory,” MIT Press, Cambridge, 1991.
[6]	J. Nash, “Equilibrium Pints in n-Person Games,” Proceedings of the National Academy of Science, Vol. 36, No. 1, 1950, pp. 48-49. http://dx.doi.org/10.1073/pnas.36.1.48
[7]	D. A. Debreu, “Social Equilibrium Existence,” Proceedings of the National Academy of Science, Vol. 38, No. 10, 1952, pp. 886-893. http://dx.doi.org/10.1073/pnas.38.10.886
[8]	R. B. Myerson, “Game Theory: Analysis of Conflict,” Harvard University, Cambridge, 1991.