IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v13y2023i3d10.1007_s13235-022-00458-8.html
   My bibliography  Save this article

Fixation Probabilities of Strategies for Trimatrix Games and Their Applications to Triadic Conflict

Author

Listed:
  • Takuya Sekiguchi

    (RIKEN)

Abstract

This study extends existing formulae of the fixation probabilities of strategies for symmetric games and bimatrix games in finite populations and derives a counterpart for trimatrix games. This allows us to describe the stochastic evolutionary game dynamics when three players are assigned different roles and therefore are not interchangeable. Following previous studies, we also derived two types of stochastic stability conditions based on the obtained fixation probabilities; “strong stochastic stability,” which requires that for any initial frequencies of strategies, the fixation probability of a combination of specific strategies is higher than that under neutrality and those of any other combinations are lower than neutrality; and “stochastic stability,” which only requires that the fixation probability of a specific strategy combination be higher than that under neutrality for any initial frequencies of strategies. Thus, for the former, we obtain a clear correspondence with bimatrix games, but not necessarily for the latter. The results of applying our findings to triadic conflicts (the Impartial person and mediator game and the Fish in troubled waters game), the volunteer’s dilemma, and coordination games are also reported.

Suggested Citation

  • Takuya Sekiguchi, 2023. "Fixation Probabilities of Strategies for Trimatrix Games and Their Applications to Triadic Conflict," Dynamic Games and Applications, Springer, vol. 13(3), pages 1005-1033, September.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:3:d:10.1007_s13235-022-00458-8
    DOI: 10.1007/s13235-022-00458-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-022-00458-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13235-022-00458-8?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. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, April.
    2. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    3. Sekiguchi, Takuya, 2013. "General conditions for strategy abundance through a self-referential mechanism under weak selection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2886-2892.
    4. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    5. Andreas Diekmann, 1985. "Volunteer's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 29(4), pages 605-610, December.
    6. Takuya Sekiguchi & Hisashi Ohtsuki, 2017. "Fixation Probabilities of Strategies for Bimatrix Games in Finite Populations," Dynamic Games and Applications, Springer, vol. 7(1), pages 93-111, March.
    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. Takuya Sekiguchi & Hisashi Ohtsuki, 2017. "Fixation Probabilities of Strategies for Bimatrix Games in Finite Populations," Dynamic Games and Applications, Springer, vol. 7(1), pages 93-111, March.
    2. Sekiguchi, Takuya, 2023. "Abundance of strategies for trimatrix games in finite populations," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    3. Marta C. Couto & Saptarshi Pal, 2023. "Introspection Dynamics in Asymmetric Multiplayer Games," Dynamic Games and Applications, Springer, vol. 13(4), pages 1256-1285, December.
    4. Chaitanya Gokhale & Arne Traulsen, 2014. "Evolutionary Multiplayer Games," Dynamic Games and Applications, Springer, vol. 4(4), pages 468-488, December.
    5. Christian Hilbe & Moshe Hoffman & Martin A. Nowak, 2015. "Cooperate without Looking in a Non-Repeated Game," Games, MDPI, vol. 6(4), pages 1-15, September.
    6. Konrad, Kai A. & Morath, Florian, 2020. "The Volunteer’s Dilemma in Finite Populations," CEPR Discussion Papers 15536, C.E.P.R. Discussion Papers.
    7. John T. Scholz & Cheng‐Lung Wang, 2009. "Learning to Cooperate: Learning Networks and the Problem of Altruism," American Journal of Political Science, John Wiley & Sons, vol. 53(3), pages 572-587, July.
    8. Xiudeng Zheng & Ross Cressman & Yi Tao, 2011. "The Diffusion Approximation of Stochastic Evolutionary Game Dynamics: Mean Effective Fixation Time and the Significance of the One-Third Law," Dynamic Games and Applications, Springer, vol. 1(3), pages 462-477, September.
    9. Zibo Xu, 2013. "The instability of backward induction in evolutionary dynamics," Discussion Paper Series dp633, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    10. Ania, Ana B. & Wagener, Andreas, 2009. "The Open Method of Coordination (OMC) as an Evolutionary Learning Process," Hannover Economic Papers (HEP) dp-416, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    11. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    12. Quan, Ji & Liu, Wei & Chu, Yuqing & Wang, Xianjia, 2018. "Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 123-134.
    13. Jacek Miȩkisz & Sergiusz Wesołowski, 2011. "Stochasticity and Time Delays in Evolutionary Games," Dynamic Games and Applications, Springer, vol. 1(3), pages 440-448, September.
    14. Sandholm, William H., 2012. "Stochastic imitative game dynamics with committed agents," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2056-2071.
    15. Nöldeke, Georg & Peña, Jorge, 2020. "Group size and collective action in a binary contribution game," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 42-51.
    16. Kai A. Konrad & Florian Morath, 2021. "The volunteer’s dilemma in finite populations," Journal of Evolutionary Economics, Springer, vol. 31(4), pages 1277-1290, September.
    17. Veller, Carl & Hayward, Laura K., 2016. "Finite-population evolution with rare mutations in asymmetric games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 93-113.
    18. Konrad, Kai A. & Morath, Florian, 2016. "Bargaining with incomplete information: Evolutionary stability in finite populations," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 118-131.
    19. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    20. Jacek Miȩkisz & Michał Matuszak & Jan Poleszczuk, 2014. "Stochastic Stability in Three-Player Games with Time Delays," Dynamic Games and Applications, Springer, vol. 4(4), pages 489-498, 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:spr:dyngam:v:13:y:2023:i:3:d:10.1007_s13235-022-00458-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.