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Existence and solution methods for equilibria

Author

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  • Bigi, Giancarlo
  • Castellani, Marco
  • Pappalardo, Massimo
  • Passacantando, Mauro

Abstract

Equilibrium problems provide a mathematical framework which includes optimization, variational inequalities, fixed-point and saddle point problems, and noncooperative games as particular cases. This general format received an increasing interest in the last decade mainly because many theoretical and algorithmic results developed for one of these models can be often extended to the others through the unifying language provided by this common format. This survey paper aims at covering the main results concerning the existence of equilibria and the solution methods for finding them.

Suggested Citation

  • Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
  • Handle: RePEc:eee:ejores:v:227:y:2013:i:1:p:1-11
    DOI: 10.1016/j.ejor.2012.11.037
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    References listed on IDEAS

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    1. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
    2. Nagurney, Anna & Ke, Ke, 2006. "Financial networks with intermediation: Risk management with variable weights," European Journal of Operational Research, Elsevier, vol. 172(1), pages 40-63, July.
    3. Zugang Liu & Anna Nagurney, 2007. "Financial Networks with Intermediation and Transportation Network Equilibria: A Supernetwork Equivalence and Reinterpretation of the Equilibrium Conditions with Computations," Computational Management Science, Springer, vol. 4(3), pages 243-281, July.
    4. Anna Nagurney, 2010. "Formulation and analysis of horizontal mergers among oligopolistic firms with insights into the merger paradox: a supply chain network perspective," Computational Management Science, Springer, vol. 7(4), pages 377-406, October.
    5. Anna Nagurney & Jose Cruz, 2003. "International financial networks with intermediation: modeling, analysis, and computations," Computational Management Science, Springer, vol. 1(1), pages 31-58, December.
    6. Zhao, Lan & Nagurney, Anna, 2008. "A network equilibrium framework for Internet advertising: Models, qualitative analysis, and algorithms," European Journal of Operational Research, Elsevier, vol. 187(2), pages 456-472, June.
    7. Giancarlo Bigi & Mauro Passacantando, 2012. "Gap functions and penalization for solving equilibrium problems with nonlinear constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 323-346, October.
    8. Dong, June & Zhang, Ding & Nagurney, Anna, 2004. "A supply chain network equilibrium model with random demands," European Journal of Operational Research, Elsevier, vol. 156(1), pages 194-212, July.
    9. Laurent Drouet & Alain Haurie & Francesco Moresino & Jean-Philippe Vial & Marc Vielle & Laurent Viguier, 2008. "An oracle based method to compute a coupled equilibrium in a model of international climate policy," Computational Management Science, Springer, vol. 5(1), pages 119-140, February.
    10. Tran Quoc & Pham Anh & Le Muu, 2012. "Dual extragradient algorithms extended to equilibrium problems," Journal of Global Optimization, Springer, vol. 52(1), pages 139-159, January.
    11. Forgo, Ferenc & Fulop, Janos & Prill, Maria, 2005. "Game theoretic models for climate change negotiations," European Journal of Operational Research, Elsevier, vol. 160(1), pages 252-267, January.
    12. Miller, Naomi & Ruszczynski, Andrzej, 2008. "Risk-adjusted probability measures in portfolio optimization with coherent measures of risk," European Journal of Operational Research, Elsevier, vol. 191(1), pages 193-206, November.
    13. Tran Quoc & Le Muu, 2012. "Iterative methods for solving monotone equilibrium problems via dual gap functions," Computational Optimization and Applications, Springer, vol. 51(2), pages 709-728, March.
    14. I. Konnov & D. Dyabilkin, 2011. "Nonmonotone equilibrium problems: coercivity conditions and weak regularization," Journal of Global Optimization, Springer, vol. 49(4), pages 575-587, April.
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    Citations

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    Cited by:

    1. Giancarlo Bigi & Mauro Passacantando, 2015. "D-gap functions and descent techniques for solving equilibrium problems," Journal of Global Optimization, Springer, vol. 62(1), pages 183-203, May.
    2. repec:spr:jglopt:v:70:y:2018:i:2:d:10.1007_s10898-017-0575-0 is not listed on IDEAS
    3. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    4. repec:spr:joptap:v:170:y:2016:i:3:d:10.1007_s10957-016-0950-x is not listed on IDEAS
    5. repec:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0187-7 is not listed on IDEAS
    6. Jean Jacques Strodiot & Phan Tu Vuong & Thi Thu Van Nguyen, 2016. "A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 64(1), pages 159-178, January.
    7. M. Castellani & M. Giuli, 2016. "Approximate solutions of quasiequilibrium problems in Banach spaces," Journal of Global Optimization, Springer, vol. 64(3), pages 615-620, March.
    8. repec:spr:joptap:v:171:y:2016:i:3:d:10.1007_s10957-016-0974-2 is not listed on IDEAS
    9. Gábor Kassay & Mihaela Miholca, 2015. "Existence results for vector equilibrium problems given by a sum of two functions," Journal of Global Optimization, Springer, vol. 63(1), pages 195-211, September.
    10. Jean Strodiot & Phan Vuong & Thi Nguyen, 2016. "A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 64(1), pages 159-178, January.
    11. Toyasaki, Fuminori & Daniele, Patrizia & Wakolbinger, Tina, 2014. "A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints," European Journal of Operational Research, Elsevier, vol. 236(1), pages 340-350.
    12. repec:spr:annopr:v:240:y:2016:i:1:d:10.1007_s10479-015-2013-3 is not listed on IDEAS
    13. Le Hai Yen & Le Dung Muu & Nguyen Thi Thanh Huyen, 2016. "An algorithm for a class of split feasibility problems: application to a model in electricity production," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 549-565, December.
    14. repec:spr:joptap:v:179:y:2018:i:1:d:10.1007_s10957-018-1319-0 is not listed on IDEAS
    15. repec:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-013-0400-y is not listed on IDEAS
    16. repec:spr:decfin:v:40:y:2017:i:1:d:10.1007_s10203-017-0188-6 is not listed on IDEAS
    17. repec:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-015-0846-1 is not listed on IDEAS
    18. Riccardi, R. & Bonenti, F. & Allevi, E. & Avanzi, C. & Gnudi, A., 2015. "The steel industry: A mathematical model under environmental regulations," European Journal of Operational Research, Elsevier, vol. 242(3), pages 1017-1027.
    19. repec:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0707-y is not listed on IDEAS
    20. Anselmi, Jonatha & Ardagna, Danilo & Passacantando, Mauro, 2014. "Generalized Nash equilibria for SaaS/PaaS Clouds," European Journal of Operational Research, Elsevier, vol. 236(1), pages 326-339.
    21. M. Castellani & M. Giuli, 2016. "Approximate solutions of quasiequilibrium problems in Banach spaces," Journal of Global Optimization, Springer, vol. 64(3), pages 615-620, March.
    22. repec:spr:joptap:v:164:y:2015:i:3:d:10.1007_s10957-013-0473-7 is not listed on IDEAS
    23. Mauro Passacantando & Danilo Ardagna & Anna Savi, 2016. "Service Provisioning Problem in Cloud and Multi-Cloud Systems," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 265-277, May.
    24. repec:eee:ejores:v:266:y:2018:i:3:p:1086-1099 is not listed on IDEAS

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