AM  Vol.4 No.12 , December 2013
A Forward-Looking Nash Game and Its Application to Achieving Pareto-Efficient Optimization
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.


Cite this paper
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.
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.

 
 
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