Modeling and Analysis Iterated Prison Dilemma Game by Grossberg Counter-Propagation Neural Network
Subject Areas : electrical and computer engineering
Gh. A. Montazer
1
*
,
N. Rastegar Ramshe
2
,
Alireza Askarzadeh
3
1 - Tarbiat Modares University
2 -
3 - دانشگاه تحصیلات تکمیلی صنعتی و فنّاوری پیشرفته کرمان
Abstract :
Most of the time effective decisions in strategic situations such as competitive issues require a non-linear mapping between stimulus and response. Artificial neural networks can be an appropriate way for modeling and solving these kinds of problems. Prison Dilemma Game is a well-known game that is proposed in game theory. This paper tries to describe how using neural network, the iterated prisoner’s dilemma game can be modeled and analyzed. To do this a Grossberg Counter-Propagation Neural Network (GCP-NN) has been designed to play this game. Results show the capability of this method in complete modeling game. The results present the efficiency of the new method in comparison with the two conventional methods: Tit For Tat (TFT) strategy and Perceptron modeled game.
[1] S. C. Sharma, Operation Research, New Dehli: Discovery Publishing House, 2006.
[2] I. K. Geckil and P. Anderson, Applied Game Theory and Strategic Behavior, London: Chapman & Hall/CRC, 2010.
[3] R. Ginevicius and A. Krivka, "Application of game theory for duopoly market analysis," J. of Business Economics and Management, vol. 9, no. 3, pp. 207-217, Oct. 2007.
[4] K. W. Lye and J. Wing, "Game strategies in network security," Int. J. of Information Security, vol. 4, no. 1-2, pp. 71-86, Feb. 2005.
[5] J. Leino, Applications of Game Theory in Ad Hoc Networks, in Department of Engineering Physics and Mathematics, Helsinki University of Technology, p. 67, 2003.
[6] A. B. Mackenzie and L. A. Dasilva, Game Theory for Wireless Engineers, Morgan & Claypool Publishers, 2006.
[7] M. Leng and M. Parlar, Game Theory Applications in Supply Chain Management: a Review, Infor, p. 220, 2005.
[8] S. Moretti, "Game theory applied to gene expression analysis," 4OR: A Quarterly Journal of Operations Research, vol. 7, no. 2, pp. 195-198, 2009.
[9] Y. Shoham and K. Leyton - Brown, Multiagent Systems Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge University Press, 2009.
[10] M. J. Osborne and A. Rubinstein, A Course in Game Theory, London, England: The MIT Press Cambridge, Massachusetts, 1994.
[11] T. Rees, An Introduction to Evolutionary Game Theory, pp. 1-4, 2005.
[12] N. Nisan, T. Roughgarden, E. Tardos, and V. Vizinari, Algorithmic Game Theory, Cambridge University Press, 2007.
[13] A. Chakeri, A. N. Dariani, and C. Lucas, "How can fuzzy logic determine game equilibriums better?" in Proc. Int. IEEE Conf. Intelligent Systems, vol. 2, pp. 51-56, 6-8 Sep. 2008.
[14] D. Garagic and J. B. Cruz, "An approach to fuzzy noncooperative nash games," Optimization Theory and Application, vol. 118, no. 3, pp. 475-491, Sep. 2003.
[15] B. Couraud and P. Liu, "Use of neural networks as decision makers in strategic situations," in Proc. of the 8th Int. Conf. on Machine Learning and Cybernetics, vol. 3, pp. 1280-1285, 12-15 Jul. 2009.
[16] M. Leshno, D. Moller, and P. Ein - Dor, "Neural nets in a group decision process," Int J. Game Theory, vol. 31, no. 3, pp. 447-467, Jun. 2003.
[17] M. Macy, "Natural selection and social learning in prisoner's dilemma: coadaptation with genetic algorithms and artificial neural networks," Sociological Methods and Research, vol. 25, no. 1, pp. 103-137, Aug. 1996.
[18] D. Sgroi and D. J. Zizzo, "Learning to play 3×3 games: neural networks as bounded-rational players," J. of Economic Behavior and Organization, vol. 69, no. 1, pp. 27-38, Jan. 2009.
[19] R. Axelrod, The Evolution of Cooperation, New York: Basic Books, 1984.
[20] R. Axelrod, "More effective choice in the iterated prisoner's dilemma," Conflict Resolution, vol. 24, no. 3, pp. 379-403, Sep. 1980.
[21] R. Hetcht-Nielsen, "Counterpropagation networks," Applied Optics, vol. 26, no. 23, pp. 4979-4984, 1987.
[22] S. C. Juang, Y. S. Tarng, and H. R. Lii, "A comparison between the back - propagation and counter - propagation networks in the modeling of the TIG welding process," J. of Materials Processing Technology, vol. 75, pp. 54-62, 1998.
[23] A. I. Margaris and E. Kotsialos, "Parallel counter-propagation networks," in Proc. of the Int. Conf. on Theory and Applications of Mathematics and Informatics, ICTAMI, pp. 306-324, Thessaloniki, Greece, 2004.
[24] J. O'Madadhain, Neural Network-Based Strategies for the Iterated Prisoner's Dilemma, Winter 2002.
[25] S. Haykin, Neural Networks a Comprehensive Foundation, Prentice Hall, 1999.
[26] L. W. Freriks, P. J. M. Cluitmans, and M. J. van Gils, The Adaptive Resonance Theory Network: (Clustering-) Behaviour in Relation with Brainstem Auditory Evoked Potential Patterns, Eindhoven University of Technology Research Reports, Netherlands, p. 113, 1992.
[27] J. D. Miller, Game Theory at Work: How to Use Game Theory to Outthink and Outmaneuver Your Competition, New York: McGraw-Hill, 2003.
[28] A. Birk and J. Wiernik, "An N-player prisoner's dilemma in a robotic ecosystem," Int. J. Robotics and Autonomous Systems, vol. 39, pp. 223-233, 2002.