IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v154y2022ics0960077921009528.html
   My bibliography  Save this article

Strange attractors and nontrivial solutions in games with three players

Author

Listed:
  • Melkikh, A.V.
  • Beregov, R.Y.
  • Sutormina, M.I.

Abstract

Two-player games have been sufficiently researched, but three-player games have a much greater wealth of solutions, in particular, nonstationary solutions. However, unsteady solutions of three-player games have not been studied in the literature. On the basis of numerical modeling, the dynamic behavior of a 2 × 2 × 2 game with three players is investigated in the range of payoff matrices from -1 to 1. The system of dynamic equations includes three variables (probabilities of pure strategies) and twelve parameters associated with cubic payoff matrices of players. The phase space of a three-player game is a cube (probabilities vary from 0 to 1). It was found that for some payoff matrices, there are no stable solutions in the system. In addition, the structure of the phase space is complex: the volume of the cube is a fractal repulsive region from which the phase trajectories leave, a strange attractor is located near the edge corresponding to the solution of the "node-center" type, and another strange attractor is a chaotic motion between adjacent vertices of the cube. The obtained dynamic properties of the game can be used for making decisions in economics, negotiations between three persons, and modeling relationships between biological species.

Suggested Citation

  • Melkikh, A.V. & Beregov, R.Y. & Sutormina, M.I., 2022. "Strange attractors and nontrivial solutions in games with three players," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009528
    DOI: 10.1016/j.chaos.2021.111598
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921009528
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111598?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chaitanya Gokhale & Arne Traulsen, 2014. "Evolutionary Multiplayer Games," Dynamic Games and Applications, Springer, vol. 4(4), pages 468-488, December.
    2. Paul M. Sweezy, 1939. "Demand Under Conditions of Oligopoly," Journal of Political Economy, University of Chicago Press, vol. 47, pages 568-568.
    3. Carlos González-Alcón & Peter Borm & Ruud Hendrickx & Kim Kuijk, 2007. "A taxonomy of best-reply multifunctions in 2×2×2 trimatrix games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 297-306, December.
    4. Stewart N. Ethier & Jiyeon Lee, 2015. "On the Three-Person Game Baccara Banque," Games, MDPI, vol. 6(2), pages 1-22, May.
    5. Hamanaka, Shintaro, 2016. "Dynamics of investment negotiations between China and Japan : the China-Japan-Korea trilateral investment treaty and beyond," IDE Discussion Papers 613, Institute of Developing Economies, Japan External Trade Organization(JETRO).
    6. Carlos González-Alcón & Peter Borm & Ruud Hendrickx, 2014. "Nash Equilibria In 2 × 2 × 2 Trimatrix Games With Identical Anonymous Best-Replies," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1-9.
    7. Aerts, Diederik & Broekaert, Jan & Czachor, Marek & Kuna, Maciej & Sinervo, Barry & Sozzo, Sandro, 2014. "Quantum structure in competing lizard communities," Ecological Modelling, Elsevier, vol. 281(C), pages 38-51.
    8. Mikhail Burtsev & Peter Turchin, 2006. "Evolution of cooperative strategies from first principles," Nature, Nature, vol. 440(7087), pages 1041-1044, April.
    9. Maciej Bukowski & Jacek Miekisz, 2004. "Evolutionary and asymptotic stability in symmetric multi-player games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 41-54, January.
    10. Guirong Liu & Rong Liu, 2019. "Dynamics of a Stochastic Three-Species Food Web Model with Omnivory and Ratio-Dependent Functional Response," Complexity, Hindawi, vol. 2019, pages 1-19, November.
    11. Waldan K. Kwong & Javier Campo & Varsha Mathur & Mark J. A. Vermeij & Patrick J. Keeling, 2019. "A widespread coral-infecting apicomplexan with chlorophyll biosynthesis genes," Nature, Nature, vol. 568(7750), pages 103-107, April.
    Full references (including those not matched with items on IDEAS)

    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. Ozgur Aydogmus & Erkan Gürpinar, 2022. "Science, Technology and Institutional Change in Knowledge Production: An Evolutionary Game Theoretic Framework," Dynamic Games and Applications, Springer, vol. 12(4), pages 1163-1188, December.
    2. Jorge Peña & Georg Nöldeke, 2023. "Cooperative Dilemmas with Binary Actions and Multiple Players," Dynamic Games and Applications, Springer, vol. 13(4), pages 1156-1193, December.
    3. 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.
    4. Alger, Ingela & Weibull, Jörgen W., 2014. "Evolution leads to Kantian morality," TSE Working Papers 14-504, Toulouse School of Economics (TSE), revised Jun 2015.
    5. Jana Fibírová, 2008. "The Competitive Advantage of Management Accounting [Konkurenční výhoda manažerského účetnictví]," Český finanční a účetní časopis, Prague University of Economics and Business, vol. 2008(2), pages 78-90.
    6. Te Wu & Feng Fu & Long Wang, 2011. "Moving Away from Nasty Encounters Enhances Cooperation in Ecological Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-7, November.
    7. Sivakumar, K. & Weigand, Robert E., 1997. "Model of retail price match guarantees," Journal of Business Research, Elsevier, vol. 39(3), pages 241-255, July.
    8. Claude d'Aspremont & Rodolphe Dos Santos Ferreira & Louis-André Gérard-Varet, 2007. "Competition For Market Share Or For Market Size: Oligopolistic Equilibria With Varying Competitive Toughness," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(3), pages 761-784, August.
    9. Ramakrushna Panigrahi, 2021. "Returns to Growth in Indian Automobile Industry: A Non-Parametric Data Envelopment Analysis (DEA) Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(4), pages 747-765, December.
    10. Chien-Ping Chen, 2009. "A Puzzle or a Choice: Uniform Pricing for Motion Pictures at the Box," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 37(1), pages 73-85, March.
    11. Han, The Anh & Traulsen, Arne & Gokhale, Chaitanya S., 2012. "On equilibrium properties of evolutionary multi-player games with random payoff matrices," Theoretical Population Biology, Elsevier, vol. 81(4), pages 264-272.
    12. Macleod, W. Bentley, 1985. "A theory of conscious parallelism," European Economic Review, Elsevier, vol. 27(1), pages 25-44, February.
    13. Alexander L. Wolman, 2007. "The frequency and costs of individual price adjustment," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(6), pages 531-552.
    14. Rudy Douven & Ron van der Heijden & Thomas McGuire & Erik Schut, 2017. "Premium levels and demand response in health insurance: relative thinking and zero-price effects," CPB Discussion Paper 366, CPB Netherlands Bureau for Economic Policy Analysis.
    15. Douven, Rudy & van der Heijden, Ron & McGuire, Thomas & Schut, Frederik, 2020. "Premium levels and demand response in health insurance: relative thinking and zero-price effects," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 903-923.
    16. Currarini, Sergio & Marini, Marco, 2011. "Kinked norms of behaviour and cooperation," Economics Letters, Elsevier, vol. 110(3), pages 223-225, March.
    17. Mariano Tommasi, 1992. "Intertemporal Pricing in Search Markets, Customer Markets and Price Rigidity," UCLA Economics Working Papers 681, UCLA Department of Economics.
    18. Manh Hong Duong & Hoang Minh Tran & The Anh Han, 2019. "On the Expected Number of Internal Equilibria in Random Evolutionary Games with Correlated Payoff Matrix," Dynamic Games and Applications, Springer, vol. 9(2), pages 458-485, June.
    19. Jones, Philip & Hudson, John, 1996. "Signalling product quality: When is price relevant?," Journal of Economic Behavior & Organization, Elsevier, vol. 30(2), pages 257-266, August.
    20. Marta C. Couto & Saptarshi Pal, 2023. "Introspection Dynamics in Asymmetric Multiplayer Games," Dynamic Games and Applications, Springer, vol. 13(4), pages 1256-1285, December.

    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:eee:chsofr:v:154:y:2022:i:c:s0960077921009528. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.