Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Nash Dominance with Applications to Equilibrium Problems with Equilibrium Constraints

  • Conference paper
Soft Computing in Industrial Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 75))

Abstract

We examine a novel idea for the detection of Nash Equilibrium developed in [15] and apply it to Equilibrium Problems with Equilibrium Constraints (EPECs). EPECs are Nash games which uniquely feature players constrained by a condition governing equilibrium of a parametric system. By redefining the selection criteria used in evolutionary methods, EPECs can be solved using Evolutionary Multiobjective Optimization algorithms. We give a proposed algorithm (NDEMO) and illustrate it with numerical examples.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Červinka, M.: Hierarchical structures in equilibrium problems. PhD Thesis, Charles University, Prague, Czech Republic (2008)

    Google Scholar 

  2. Chellapilla, K., Fogel, D.: Evolving neural networks to play checkers without expert knowledge. IEEE Transactions on Neural Networks 10(6), 1382–1391 (1999)

    Article  Google Scholar 

  3. Coello-Coello, C., Lamont, G.: Applications of multi-objective evolutionary algorithms. World Scientific, Singapore (2004)

    MATH  Google Scholar 

  4. Curzon Price, T.: Using co-evolutionary programming to simulate strategic behavior in markets. Journal of Evolutionary Economics 7(3), 219–254 (1997)

    Article  Google Scholar 

  5. Deb, K.: Multi-objective optimization using evolutionary algorithms. John Wiley, Chichester (2001)

    MATH  Google Scholar 

  6. Facchinei, F., Kanzow, C.: Generalized Nash equilibrium problems. 4OR 5(3), 173–210 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gabay, D., Moulin, H.: On the uniqueness and stability of Nash-equilibria in non cooperative games. In: Bensoussan, A., et al. (eds.) Applied Stochastic Control in Econometrics and Management Science, pp. 271–293. North Holland, Amsterdam (1980)

    Google Scholar 

  8. Harker, P.T.: A variational inequality approach for the determination of Oligopolistic market equilibrium. Mathematical Programming 30(1), 105–111 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hu, X., Ralph, D.: Using EPECs to model bilevel games in restructured electricity markets with locational prices. Operations Research 55(5), 809–827 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Judd, K.: Numerical methods in Economics. MIT Press, Cambridge (1998)

    MATH  Google Scholar 

  11. Karamardian, S.: Generalized complementarity problems. Journal of Optimization Theory and Applications 8(3), 161–168 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  12. Koh, A.: Coevolutionary particle swarm algorithm for bi-level variational inequalities: applications to competition in highway transportation networks. In: Chiong, R., Dhakal, S. (eds.) Natural intelligence for scheduling, planning and packing problems, pp. 195–217. Springer, Berlin (2009)

    Chapter  Google Scholar 

  13. Koh, A., Shepherd, S.: Tolling, collusion and equilibrium problems with equilibrium constraints. European Transport/Trasporti Europei (in press)

    Google Scholar 

  14. Kolstad, M., Mathisen, L.: Computing Cournot-Nash equilibrium. Operations Research 39(5), 739–748 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lung, R.I., Dumitrescu, D.: Computing Nash equilibria by means of evolutionary computation. International Journal of Computers, Commmunications and Control III, 364–368 (2008)

    Google Scholar 

  16. Mordukhovich, B.S.: Optimization and equilibrium problems with equilibrium constraints. Omega 33(5), 379–384 (2005)

    Article  Google Scholar 

  17. Mordukhovich, B.S.: Variational analysis and generalized Differentiation, II: Applications. Grundlehren der mathematischen wissenschaften, vol. 331. Springer, Berlin (2006)

    Google Scholar 

  18. Nash, J.: Equilibrium points in N-person games. Proceedings of the National Academy of Science USA 36(1), 48–49 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  19. Pedroso, J.P.: Numerical solution of Nash and Stackelberg equilibria: an evolutionary approach. In: Proceedings of SEAL 1996, pp. 151–160 (1996)

    Google Scholar 

  20. Potter, M.A., De Jong, K.: A cooperative coevolutionary approach for function optimization. In: Proceedings of PPSN III, pp. 249–257. Springer, Berlin (1994)

    Google Scholar 

  21. Price, K., Storn, R., Lampinen, J.: Differential evolution: a practical approach to global optimization. Springer, Berlin (2005)

    MATH  Google Scholar 

  22. Protopapas, M., Kosmatopoulos, E.: Determination of sequential best replies in n-player games by genetic algorithms. International Journal of Applied Mathematics and Computer Science 5(1), 19–24 (2009)

    Google Scholar 

  23. Rajabioun, R., Atashpaz-Gargari, E., Lucas, C.: Colonial competitive algorithm as a tool for Nash equilibrium point achievement. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds.) ICCSA 2008, Part II. LNCS, vol. 5073, pp. 680–695. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  24. Rapoport, A., Chammah, A.: Prisoner’s Dilemma. University of Michigan Press, Ann Arbour (1965)

    Google Scholar 

  25. Razi, K., Shahri, S.H., Kian, A.R.: Finding Nash equilibrium point of nonlinear non-cooperative games using coevolutionary strategies. In: Proceedings of ISDA, pp. 875–882 (2007)

    Google Scholar 

  26. Robič, T., Filipič, B.: DEMO: differential evolution for multiobjective problems. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005)

    Google Scholar 

  27. Sefrioui, M., Periaux, J.: Nash genetic algorithms: examples and applications. In: Proceedings of IEEE CEC, pp. 509–516 (2000)

    Google Scholar 

  28. Son, Y., Baldick, R.: Hybrid coevolutionary programming for Nash equilibrium search in games with local optima. IEEE Transactions on Evolutionary Computation 8(4), 305–315 (2004)

    Article  Google Scholar 

  29. Su, C.: Equilibrium problems with equilibrium constraints: stationarities, algorithms and applications. PhD Thesis, Stanford University, California, USA (2005)

    Google Scholar 

  30. Wardrop, J.G.: Some theoretical aspects of road traffic research. Proceedings of Institution of Civil Engineers Part II 1(36), 325–378 (1952)

    Google Scholar 

  31. Webb, J.N.: Game theory: decisions, interaction and Evolution. Springer, London (2007)

    MATH  Google Scholar 

  32. Yang, H., Feng, X., Huang, H.: Private road competition and equilibrium with traffic equilibrium constraints. Journal of Advanced Transportation 43(1), 21–45 (2009)

    Article  Google Scholar 

  33. Zubeita, L.: A network equilibrium model for oligopolistic competition in city bus services. Transportation Research Part B 32(6), 413–422 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Transport Studies, University of Leeds, Leeds, LS2 9JT, United Kingdom

    Andrew Koh

Authors
  1. Andrew Koh
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Helsinki University, Espoo, Finland

    Xiao-Zhi Gao

  2. University of Minho, Giumaraes, Portugal

    António Gaspar-Cunha

  3. Kyushu Inst. of Technology, Fukuoka, Japan

    Mario Köppen

  4. Loughborough University, Loughborough, UK

    Gerald Schaefer

  5. The Chinese University of Hong Kong, Hong Kong

    Jun Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Koh, A. (2010). Nash Dominance with Applications to Equilibrium Problems with Equilibrium Constraints. In: Gao, XZ., Gaspar-Cunha, A., Köppen, M., Schaefer, G., Wang, J. (eds) Soft Computing in Industrial Applications. Advances in Intelligent and Soft Computing, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11282-9_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11282-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11281-2

  • Online ISBN: 978-3-642-11282-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation