IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v685y2026ics0378437125009100.html

Bounded rationality produces Nash equilibria in sports networks: Protection, learning, and strategic adaptation

Author

Listed:
  • Park, Chulwook
  • Fath, Brian D.

Abstract

Complex systems exhibit strategic interactions in which risk propagation is influenced by networked relationships. This study presents a network–agent model within sports contexts, demonstrating how Nash equilibria emerge from bounded rationality. Using scale-free networks where nodes represent sports agents, we simulate evolutionary game dynamics under varying protection and learning parameters. The model reveals four distinct equilibria: coexistence with sufficient protection, system-wide failure under low protection, partial coexistence with limited protection, and robust protection with minimal failure. The balance between social learning and strategic adaptation crucially determines system behavior; low values produce fragmented strategic clusters, whereas high values drive convergence toward uniform protection strategies. Nash equilibria naturally emerge when competitive outcomes coexist with cooperative protection behaviors, offering practical insights for sports practitioners on prevention strategies, knowledge transfer, and the emergence of complementary specialized roles within teams.

Suggested Citation

  • Park, Chulwook & Fath, Brian D., 2026. "Bounded rationality produces Nash equilibria in sports networks: Protection, learning, and strategic adaptation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 685(C).
    • Handle: RePEc:eee:phsmap:v:685:y:2026:i:c:s0378437125009100
    DOI: 10.1016/j.physa.2025.131258
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437125009100
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2025.131258?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
    2. George J. Mailath, 1998. "Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1347-1374, September.
    3. Guo, H. & Jia, D. & Sendiña-Nadal, I. & Zhang, M. & Wang, Z. & Li, X. & Alfaro-Bittner, K. & Moreno, Y. & Boccaletti, S., 2021. "Evolutionary games on simplicial complexes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. O. G. Haywood, 1954. "Military Decision and Game Theory," Operations Research, INFORMS, vol. 2(4), pages 365-385, November.
    5. Vicki M. Bier, 2007. "Choosing What to Protect," Risk Analysis, John Wiley & Sons, vol. 27(3), pages 607-620, June.
    6. Aaron Smith & Hans Westerbeek, 2004. "The Sport Business Future," Palgrave Macmillan Books, Palgrave Macmillan, number 978-0-230-51369-3, September.
    7. Kenneth Kovash & Steven D. Levitt, 2009. "Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League," NBER Working Papers 15347, National Bureau of Economic Research, Inc.
    8. Chulwook Park, 2025. "Optimizing Resilience in Sports Science Through an Integrated Random Network Structure: Harnessing the Power of Failure, Payoff, and Social Dynamics," SAGE Open, , vol. 15(1), pages 21582440251, February.
    9. Marco Tortoriello & Ray Reagans & Bill McEvily, 2012. "Bridging the Knowledge Gap: The Influence of Strong Ties, Network Cohesion, and Network Range on the Transfer of Knowledge Between Organizational Units," Organization Science, INFORMS, vol. 23(4), pages 1024-1039, August.
    10. Chulwook Park, 2020. "Network and Agent Dynamics with Evolving Protection against Systemic Risk," Complexity, Hindawi, vol. 2020, pages 1-16, March.
    11. Arthur, W Brian, 1991. "Designing Economic Agents that Act Like Human Agents: A Behavioral Approach to Bounded Rationality," American Economic Review, American Economic Association, vol. 81(2), pages 353-359, May.
    12. Ho Fai Chan & David A. Savage & Benno Torgler, 2021. "Sport as a Behavioral Economics Lab," CREMA Working Paper Series 2021-20, Center for Research in Economics, Management and the Arts (CREMA).
    13. Mengke Zhang & Yan Huang & Yifan Jin & Yuan Bao, 2023. "Government regulation strategy, leading firms’ innovation strategy, and following firms imitation strategy: An analysis based on evolutionary game theory," PLOS ONE, Public Library of Science, vol. 18(6), pages 1-27, June.
    14. David J. Teece, 2007. "Explicating dynamic capabilities: the nature and microfoundations of (sustainable) enterprise performance," Strategic Management Journal, Wiley Blackwell, vol. 28(13), pages 1319-1350, December.
    15. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    16. Daniel A Braun & Pedro A Ortega & Daniel M Wolpert, 2009. "Nash Equilibria in Multi-Agent Motor Interactions," PLOS Computational Biology, Public Library of Science, vol. 5(8), pages 1-8, August.
    17. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
    18. Silvana M. Pesenti & Sebastian Jaimungal & Yuri F. Saporito & Rodrigo S. Targino, 2023. "Risk Budgeting Allocation for Dynamic Risk Measures," Papers 2305.11319, arXiv.org, revised Oct 2024.
    19. Prajit K. Dutta, 1999. "Strategies and Games: Theory and Practice," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262041693, December.
    20. Leduc, Matt V. & Momot, Ruslan, 2017. "Strategic investment in protection in networked systems," Network Science, Cambridge University Press, vol. 5(1), pages 108-139, March.
    21. Ofer Azar & Michael Bar-Eli, 2011. "Do soccer players play the mixed-strategy Nash equilibrium?," Applied Economics, Taylor & Francis Journals, vol. 43(25), pages 3591-3601.
    22. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    23. Stefan Szymanski, 2010. "The Economic Design of Sporting Contests," Palgrave Macmillan Books, in: The Comparative Economics of Sport, chapter 1, pages 1-78, Palgrave Macmillan.
    24. Bar-Eli, Michael & Azar, Ofer H. & Ritov, Ilana & Keidar-Levin, Yael & Schein, Galit, 2007. "Action bias among elite soccer goalkeepers: The case of penalty kicks," Journal of Economic Psychology, Elsevier, vol. 28(5), pages 606-621, October.
    25. George J. Mailath, 1998. "Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1347-1374, September.
    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. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2017. "Serial correlation in National Football League play calling and its effects on outcomes," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 69(C), pages 125-132.
    2. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    3. Sean Duffy & J. J. Naddeo & David Owens & John Smith, 2024. "Cognitive Load and Mixed Strategies: On Brains and Minimax," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 1-34, September.
    4. Larry Samuelson, 2004. "Modeling Knowledge in Economic Analysis," Journal of Economic Literature, American Economic Association, vol. 42(2), pages 367-403, June.
    5. Alexandre Bevilacqua Leoneti & René Bañares-Alcántara & Eduardo Cleto Pires & Sonia Valle Walter Borges Oliveira, 2022. "A Multi-Criteria and Multi-Agent Framework for supporting complex decision-making processes," Group Decision and Negotiation, Springer, vol. 31(5), pages 1025-1050, October.
    6. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2014. "Minimax on the gridiron: Serial correlation and its effects on outcomes in the National Football League," MPRA Paper 58907, University Library of Munich, Germany.
    7. Daniel John Zizzo & Daniel Sgroi, 2001. "Bounded-Rational Behavior by Neural Networks in Normal Form Games," Economics Series Working Papers 2000-W30, University of Oxford, Department of Economics.
    8. Ball, Richard, 2017. "Violations of monotonicity in evolutionary models with sample-based beliefs," Economics Letters, Elsevier, vol. 152(C), pages 100-104.
    9. David Schüller & Thorsten Upmann, 2013. "When Focal Points are Out of Focus: A Game-Theoretic Analysis of Come Dine with Me," CESifo Working Paper Series 4138, CESifo.
    10. Sent, Esther-Mirjam, 2004. "The legacy of Herbert Simon in game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 53(3), pages 303-317, March.
    11. Alberto Locarno, 2012. "Monetary policy in a model with misspecified, heterogeneous and ever-changing expectations," Temi di discussione (Economic working papers) 888, Bank of Italy, Economic Research and International Relations Area.
    12. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    13. Battigalli, Pierpaolo & Leonetti, Paolo & Maccheroni, Fabio, 2020. "Behavioral equivalence of extensive game structures," Games and Economic Behavior, Elsevier, vol. 121(C), pages 533-547.
    14. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    15. Diego Iribarren, 2003. "From Economic Activity to Understanding Spaces," EERI Research Paper Series EERI_RP_2003_01, Economics and Econometrics Research Institute (EERI), Brussels.
    16. Thijssen, J.J.J., 2003. "Investment under uncertainty, market evolution and coalition spillovers in a game theoretic perspective," Other publications TiSEM 672073a6-492e-4621-8d4a-0, Tilburg University, School of Economics and Management.
    17. Christian Ewerhart & Stanisław Kaźmierowski, 2024. "An equilibrium analysis of the Arad-Rubinstein game," ECON - Working Papers 443, Department of Economics - University of Zurich.
    18. Heifetz, Aviad & Heller, Ruth & Ostreiher, Roni, 2021. "Do Arabian babblers play mixed strategies in a “volunteer’s dilemma”?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 91(C).
    19. Burkhard C. Schipper & Hang Zhou, 2026. "Level-k thinking in the extensive form," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 81(1), pages 149-189, February.
    20. Bodo Herzog & Stefanie Schnee, 2022. "Exploring a Dualism of Human Rationality: Experimental Study of a Cheating Contest Game," IJERPH, MDPI, vol. 19(13), pages 1-13, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:phsmap:v:685:y:2026:i:c:s0378437125009100. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.