IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v9y2018i3p46-d156807.html
   My bibliography  Save this article

Computation of Sparse and Dense Equilibrium Strategies of Evolutionary Games

Author

Listed:
  • Yiping Hao

    (Department of Mathematics, Iowa State University, Ames, IA 50011, USA
    These authors contributed equally to this work.)

  • Zhijun Wu

    (Department of Mathematics, Iowa State University, Ames, IA 50011, USA
    These authors contributed equally to this work.)

Abstract

The evolution of social or biological species can be modeled as an evolutionary game with the equilibrium strategies of the game as prediction for the ultimate distributions of species in population, when some species may survive with positive proportions, while others become extinct. We say a strategy is dense if it contains a large and diverse number of positive species, and is sparse if it has only a few dominant ones. Sparse equilibrium strategies can be found relatively easily, while dense ones are more computationally costly. Here we show that by formulating a “complementary” problem for the computation of equilibrium strategies, we are able to reduce the cost for computing dense equilibrium strategies much more efficiently. We describe the primary and complementary algorithms for computing dense as well as sparse equilibrium strategies, and present test results on randomly generated games as well as a more biologically related one. In particular, we demonstrate that the complementary algorithm is about an order of magnitude faster than the primary algorithm to obtain the dense equilibrium strategies for all our test cases.

Suggested Citation

  • Yiping Hao & Zhijun Wu, 2018. "Computation of Sparse and Dense Equilibrium Strategies of Evolutionary Games," Games, MDPI, vol. 9(3), pages 1-15, July.
    • Handle: RePEc:gam:jgames:v:9:y:2018:i:3:p:46-:d:156807
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/9/3/46/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/9/3/46/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. D. Timothy Bishop & Mark Broom & Richard Southwell, 2020. "Chris Cannings: A Life in Games," Dynamic Games and Applications, Springer, vol. 10(3), pages 591-617, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, vol. 203(3), pages 635-639, June.
    2. Thomas Demuynck, 2014. "The computational complexity of rationalizing Pareto optimal choice behavior," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 529-549, March.
    3. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    4. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    5. Borgs, Christian & Chayes, Jennifer & Immorlica, Nicole & Kalai, Adam Tauman & Mirrokni, Vahab & Papadimitriou, Christos, 2010. "The myth of the Folk Theorem," Games and Economic Behavior, Elsevier, vol. 70(1), pages 34-43, September.
    6. DeCanio, Stephen J. & Fremstad, Anders, 2013. "Game theory and climate diplomacy," Ecological Economics, Elsevier, vol. 85(C), pages 177-187.
    7. Steffen Eibelshäuser & Victor Klockmann & David Poensgen & Alicia von Schenk, 2023. "The Logarithmic Stochastic Tracing Procedure: A Homotopy Method to Compute Stationary Equilibria of Stochastic Games," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1511-1526, November.
    8. Tim Roughgarden, 2018. "Complexity Theory, Game Theory, and Economics: The Barbados Lectures," Papers 1801.00734, arXiv.org, revised Feb 2020.
    9. Tim Roughgarden, 2010. "Computing equilibria: a computational complexity perspective," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 193-236, January.
    10. Martin Shubik, 2011. "The Present and Future of Game Theory," Levine's Working Paper Archive 786969000000000173, David K. Levine.
    11. Itzhak Gilboa & Ehud Kalai & Eitan Zemel, 1989. "The Complexity of Eliminating Dominated Strategies," Discussion Papers 853, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. McLennan, Andrew & Tourky, Rabee, 2010. "Simple complexity from imitation games," Games and Economic Behavior, Elsevier, vol. 68(2), pages 683-688, March.
    13. Rahul Savani & Bernhard Stengel, 2015. "Game Theory Explorer: software for the applied game theorist," Computational Management Science, Springer, vol. 12(1), pages 5-33, January.
    14. Guzmán, Cristóbal & Riffo, Javiera & Telha, Claudio & Van Vyve, Mathieu, 2022. "A sequential Stackelberg game for dynamic inspection problems," European Journal of Operational Research, Elsevier, vol. 302(2), pages 727-739.
    15. Ehud Kalai, 1995. "Games," Discussion Papers 1141, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    16. Laurens Debo & Senthil Veeraraghavan, 2014. "Equilibrium in Queues Under Unknown Service Times and Service Value," Operations Research, INFORMS, vol. 62(1), pages 38-57, February.
    17. Fernando Oliveira, 2010. "Bottom-up design of strategic options as finite automata," Computational Management Science, Springer, vol. 7(4), pages 355-375, October.
    18. Kirchsteiger, G. & Prat, A., 1999. "Common Agency and Computational Complexity : Theory and Experimental Evidence," Discussion Paper 1999-36, Tilburg University, Center for Economic Research.
    19. Hau Chan & Michael Ceyko & Luis Ortiz, 2017. "Interdependent Defense Games with Applications to Internet Security at the Level of Autonomous Systems," Games, MDPI, vol. 8(1), pages 1-60, February.
    20. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jgames:v:9:y:2018:i:3:p:46-:d:156807. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.