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Berge-Zhukovskii Optimal Nash Equilibria

  • Conference paper
EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation V

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 288))

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Abstract

The Berge-Zhukovskii optimal Nash equilibrium combines the properties of the popular Nash equilibrium with the ones of the less known Berge-Zhukovskii by proposing yet another Nash equilibrium refinement. Moreover, a computational approach for the detection of these newly proposed equilibria is presented with examples for two auction games.

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References

  1. Abalo, K., Kostreva, M.: Berge equilibrium: some recent results from fixed-point theorems. Applied Mathematics and Computation 169, 624–638 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aumann, R.J.: Acceptable points in general cooperative n-person games. In: Luce, R.D., Tucker, A.W. (eds.) Contribution to the Theory of Game IV. Annals of Mathematical Study, vol. 40, pp. 287–324. University Press (1959)

    Google Scholar 

  3. Berge, C.: Théorie générale des jeux? n personnes. Gauthier-Villars (1957)

    Google Scholar 

  4. Douglas Bernheim, B., Peleg, B., Whinston, M.D.: Coalition-proof Nash Equilibria I. Concepts. Journal of Economic Theory 42(1), 1–12 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  5. Colman, A.M., Korner, T.W., Musy, O., Tazdait, T.: Mutual support in games: Some properties of Berge equilibria. Journal of Mathematical Psychology 55(2), 166–175 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. Das, S., Suganthan, P.N.: Differential evolution: A survey of the state-of-the-art. IEEE Trans. Evolutionary Computation 15(1), 4–31 (2011)

    Article  Google Scholar 

  7. Easley, D., Kleinberg, J.: Networks, crowds, and markets: Reasoning about a highly connected world (2012)

    Google Scholar 

  8. Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms. ii. application example. IEEE Transactions on Systems Man and Cybernetics Part A Systems and Humans 28, 38–47 (1998)

    Article  Google Scholar 

  9. Gaskó, N., Dumitrescu, D., Lung, R.I.: Evolutionary Detection of Berge and Nash Equilibria. In: Pelta, D.A., Krasnogor, N., Dumitrescu, D., Chira, C., Lung, R. (eds.) NICSO 2011. SCI, vol. 387, pp. 149–158. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Gaskó, N., Suciu, M.A., Lung, R.I., Dumitrescu, D.: Dynamic Generalized Berge-Zhukovskii equilibrium detection. In: Emmerich, M., et al. (eds.) A Bridge between Probability, Set Oriented Optimization, and Evolutionary Computation (EVOLVE), pp. 53–58 (2013)

    Google Scholar 

  11. Halpern, J.Y.: Beyond nash equilibrium: Solution concepts for the 21st century. In: Proceedings of the Twenty-Seventh ACM Symposium on Principles of Distributed Computing, pp. 1–10. ACM (2008)

    Google Scholar 

  12. Klemperer, P.: Auction theory: A guide to the literature. Journal of Economic Surveys 13(3), 227–286 (1999)

    Article  Google Scholar 

  13. Levin, J.: Auction theory (2004)

    Google Scholar 

  14. Lung, R.I., Dumitrescu, D.: Computing nash equilibria by means of evolutionary computation. Int. J. of Computers, Communications & Control 6, 364–368 (2008)

    Google Scholar 

  15. Lung, R.I., Dumitrescu, D.: A new evolutionary approach to minimax problems. In: 2011 IEEE Congress on Evolutionary Computation (CEC), pp. 1902–1905. IEEE (2011)

    Google Scholar 

  16. Nash, J.: Non-Cooperative Games. The Annals of Mathematics 54(2), 286–295 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  17. Osborne, M.J.: An Introduction to Game Theory. Oxford University Press (2004)

    Google Scholar 

  18. Parsons, S., Rodriguez-Aguilar, J.A., Klein, M.: Auctions and bidding: A guide for computer scientists. ACM Comput. Surv. 43(2), 10:1–10:59 (2011)

    Google Scholar 

  19. Suciu, M., Lung, R.I., Gaskó, N., Dumitrescu, D.: Differential evolution for discrete-time large dynamic games. In: 2013 IEEE Conference on Evolutionary Computation, June 20-23, vol. 1, pp. 2108–2113 (2013)

    Google Scholar 

  20. Thomsen, R.: Multimodal optimization using crowding-based differential evolution. In: IEEE Proceedings of the Congress on Evolutionary Computation (CEC 2004), pp. 1382–1389 (2004)

    Google Scholar 

  21. Zhukovskii, V.I., Chikrii, A.A.: Linear-quadratic differential games. In: Naukova Dumka, Kiev (1994)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Babes-Bolyai University of Cluj-Napoca, Cluj-Napoca, Romania

    Noémi Gaskó, Mihai Suciu, Rodica Ioana Lung & Dan Dumitrescu

Authors
  1. Noémi Gaskó
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  2. Mihai Suciu
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  3. Rodica Ioana Lung
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  4. Dan Dumitrescu
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Editor information

Editors and Affiliations

  1. Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, Luxembourg, Luxembourg

    Alexandru-Adrian Tantar

  2. Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg, Luxembourg, Luxembourg

    Emilia Tantar

  3. School of Engineering, University of California, Merced, California, USA

    Jian-Qiao Sun

  4. College of Mechanical Engineering, Beijing University of Technology, Beijing, China

    Wei Zhang

  5. Department of Mechanics, Tianjin University, Tianjin, China

    Qian Ding

  6. Depto. Computación, CINVESTAV-IPN, Mexico City, Mexico

    Oliver Schütze

  7. Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands

    Michael Emmerich

  8. Université de Bordeaux, Bordeaux, France

    Pierrick Legrand

  9. School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia

    Pierre Del Moral

  10. Computer Science Department, CINVESTAV-IPN, Mexico City, Mexico

    Carlos A. Coello Coello

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Gaskó, N., Suciu, M., Lung, R.I., Dumitrescu, D. (2014). Berge-Zhukovskii Optimal Nash Equilibria. In: Tantar, AA., et al. EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation V. Advances in Intelligent Systems and Computing, vol 288. Springer, Cham. https://doi.org/10.1007/978-3-319-07494-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-07494-8_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07493-1

  • Online ISBN: 978-3-319-07494-8

  • eBook Packages: EngineeringEngineering (R0)

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