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Stochastic Nash Equilibrium with a Numerical Solution Method

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Advances in Neural Networks – ISNN 2005 (ISNN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3496))

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Abstract

Recent decades viewed increasing interests in the subject of decentralized decision-making. In this paper, three definitions of stochastic Nash equilibrium, which casts different decision criteria, are proposed for a stochastic decentralized decision system. Then the problem of how to find the stochastic Nash equilibrium is converted to an optimization problem. Lastly, a solution method combined with neural network and genetic algorithm is provided.

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References

  1. Anupindi, R., Bassok, Y., Zemel, E.: A General Framework for the Study of Decentralized Distribution Systems. Manufacturing & Service Operations Management 3, 349–368 (2001)

    Article  Google Scholar 

  2. Bylka, S.: Competitive and Cooperative Policies for the Vendor-buyer System. International Journal of Production Economics 81-82, 533–544 (2003)

    Article  Google Scholar 

  3. Charnes, A., Cooper, W.W.: Chance-constrained Programming. Management Science 6, 73–79 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cybenko, G.: Approximations by Superpositions of a Sigmoidal Function. Mathematics of Control, Signals and Systems 2, 183–192 (1989)

    Article  MathSciNet  Google Scholar 

  5. Gao, J., Liu, B., Gen, M.: A Hybrid Intelligent Algorithm for Stochastic Multilevel Programming. Transactions of the Institute of Electrical Engineers of Japan 124-C, 1991–1998 (2004)

    Google Scholar 

  6. Goldberg, D.E.: Genetic Algorithms in Search. In: Optimization and Machine Learning, Addison-Wesley, MA (1989)

    Google Scholar 

  7. Hirasawa, K., Yamamoto, Y., Hu, J., Murata, J., Jin, C.: Optimization of Decentralized Control System Using Nash Equilibrium Concept. Transactions of the Institute of Electrical Engineers of Japan 119-C, 467–473 (1999)

    Google Scholar 

  8. Hornik, K., Stinchcombe, M., White, H.: Multilayer Feedforward Networks are Universal Approximators. Neural Networks 2, 359–366 (1989)

    Article  Google Scholar 

  9. Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  10. Ji, X., Wang, C.: Nash Equilibrium in the Game of Transmission Expansion. In: Proceedings of 2002 IEEE Region 10 Conference on Computer, Communications, Control and Power Engineering, vol. 3, pp. 1768–1771 (2002)

    Google Scholar 

  11. Liu, B.: Dependent-chance Programming: A Class of Stochastic Programming. Comput. Math. Appl. 34, 89–104 (1997)

    Article  MATH  Google Scholar 

  12. Vriend, N.J.: A Model of Market-making. European Journal of Economic and Social Systems 15, 185–202 (2002)

    Article  Google Scholar 

  13. Wang, H., Guo, M., Efstathiou, J.: A Game-theoretical Cooperative Mechanism Design for a Two-echelon Decentralized Supply Chain. European Journal of Operational Research 157, 372–388 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Uncertain Systems Laboratory, School of Information, Renmin University of China, Beijing, 100872, China

    Jinwu Gao

  2. College of Mathematics and Computer Science, Hebei University, Baoding, 071002, China

    Yankui Liu

Authors
  1. Jinwu Gao
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  2. Yankui Liu
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Editor information

Editors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  2. The Key Laboratory of Optoelectric Technology & Systems, Ministry of Education, China

    Xiaofeng Liao

  3. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

    Zhang Yi

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© 2005 Springer-Verlag Berlin Heidelberg

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Gao, J., Liu, Y. (2005). Stochastic Nash Equilibrium with a Numerical Solution Method. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_130

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  • DOI: https://doi.org/10.1007/11427391_130

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25912-1

  • Online ISBN: 978-3-540-32065-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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