IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/90811.html
   My bibliography  Save this paper

Evolutionary stability of behavioural rules in bargaining

Author

Listed:
  • Khan, Abhimanyu

Abstract

I study the evolutionary stability of behavioural rules in a bargaining game. Individuals draw random samples of strategies used in the past and respond to it by using a behavioural rule. Even though individuals actually respond to historical demands, a necessary condition for stability is the existence of a state such that it is as-if the individuals are hardwired to make the same demand. Furthermore, the state where all individuals demand half of the pie is the unique neutrally stable state; all other states are unstable in the face of an invasion by a mutant behavioural rule.

Suggested Citation

  • Khan, Abhimanyu, 2018. "Evolutionary stability of behavioural rules in bargaining," MPRA Paper 90811, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:90811
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/90811/1/MPRA_paper_90811.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Agastya, Murali, 1999. "Perturbed Adaptive Dynamics in Coalition Form Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 207-233, December.
    3. Abhimanyu Khan & Ronald Peeters, 2014. "Cognitive hierarchies in adaptive play," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 903-924, November.
    4. Matros, Alexander, 2003. "Clever agents in adaptive learning," Journal of Economic Theory, Elsevier, vol. 111(1), pages 110-124, July.
    5. Khan, Abhimanyu, 2018. "Games between responsive behavioural rules," MPRA Paper 90429, University Library of Munich, Germany.
    6. Tore Ellingsen, 1997. "The Evolution of Bargaining Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 581-602.
    7. Pradelski, Bary S.R. & Young, H. Peyton, 2012. "Learning efficient Nash equilibria in distributed systems," Games and Economic Behavior, Elsevier, vol. 75(2), pages 882-897.
    8. Rozen, Kareen, 2013. "Conflict leads to cooperation in demand bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 87(C), pages 35-42.
    9. Ken Binmore & Larry Samuelson & Petyon Young, 2003. "Equilibrium Selection in Bargaining Models," Levine's Bibliography 506439000000000466, UCLA Department of Economics.
    10. Murali Agastya, 1997. "Adaptive Play in Multiplayer Bargaining Situations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 411-426.
    11. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
    12. Hwang, Sung-Ha & Lim, Wooyoung & Neary, Philip & Newton, Jonathan, 2018. "Conventional contracts, intentional behavior and logit choice: Equality without symmetry," Games and Economic Behavior, Elsevier, vol. 110(C), pages 273-294.
    13. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    14. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    15. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
    16. Abhimanyu Khan, 2021. "Evolution of conventions in games between behavioural rules," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 209-224, October.
    17. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    18. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    19. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    20. Josephson, Jens, 2009. "Stochastic adaptation in finite games played by heterogeneous populations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1543-1554, August.
    21. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    22. Sawa, Ryoji, 2019. "Stochastic stability under logit choice in coalitional bargaining problems," Games and Economic Behavior, Elsevier, vol. 113(C), pages 633-650.
    23. Kaniovski, Yuri M. & Kryazhimskii, Arkadii V. & Young, H. Peyton, 2000. "Adaptive Dynamics in Games Played by Heterogeneous Populations," Games and Economic Behavior, Elsevier, vol. 31(1), pages 50-96, April.
    24. Arnold, Tone & Schwalbe, Ulrich, 2002. "Dynamic coalition formation and the core," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 363-380, November.
    25. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
    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. Abhimanyu Khan, 2021. "Evolution of conventions in games between behavioural rules," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 209-224, October.

    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. Sawa, Ryoji, 2021. "A prospect theory Nash bargaining solution and its stochastic stability," Journal of Economic Behavior & Organization, Elsevier, vol. 184(C), pages 692-711.
    2. Khan, Abhimanyu, 2022. "Expected utility versus cumulative prospect theory in an evolutionary model of bargaining," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    3. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    4. Hwang, Sung-Ha & Lim, Wooyoung & Neary, Philip & Newton, Jonathan, 2018. "Conventional contracts, intentional behavior and logit choice: Equality without symmetry," Games and Economic Behavior, Elsevier, vol. 110(C), pages 273-294.
    5. Maria Montero & Alex Possajennikov, 2021. "An Adaptive Model of Demand Adjustment in Weighted Majority Games," Games, MDPI, vol. 13(1), pages 1-17, December.
    6. Sawa, Ryoji, 2019. "Stochastic stability under logit choice in coalitional bargaining problems," Games and Economic Behavior, Elsevier, vol. 113(C), pages 633-650.
    7. Heinrich Nax & Bary Pradelski, 2015. "Evolutionary dynamics and equitable core selection in assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 903-932, November.
    8. Hwang, Sung-Ha & Rey-Bellet, Luc, 2021. "Positive feedback in coordination games: Stochastic evolutionary dynamics and the logit choice rule," Games and Economic Behavior, Elsevier, vol. 126(C), pages 355-373.
    9. Heinrich Nax, 2015. "Equity dynamics in bargaining without information exchange," Journal of Evolutionary Economics, Springer, vol. 25(5), pages 1011-1026, November.
    10. repec:syd:wpaper:2123/9993 is not listed on IDEAS
    11. Nax, Heinrich H. & Pradelski, Bary S. R., 2015. "Evolutionary dynamics and equitable core selection in assignment games," LSE Research Online Documents on Economics 65428, London School of Economics and Political Science, LSE Library.
    12. Maria Montero & Alex Possajennikov, 2022. ""Greedy" Demand Adjustment in Cooperative Games," Discussion Papers 2022-05, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    13. Nax, Heinrich H., 2015. "Equity dynamics in bargaining without information exchange," LSE Research Online Documents on Economics 65426, London School of Economics and Political Science, LSE Library.
    14. Rozen, Kareen, 2008. "Conflict Leads to Cooperation in Nash Bargaining," Working Papers 39, Yale University, Department of Economics.
    15. Heinrich H. Nax & Bary S. R. Pradelski & H. Peyton Young, 2013. "The Evolution of Core Stability in Decentralized Matching Markets," Working Papers 2013.50, Fondazione Eni Enrico Mattei.
    16. Herbert Dawid & Joern Dermietzel, 2006. "How Robust is the Equal Split Norm? Responsive Strategies, Selection Mechanisms and the Need for Economic Interpretation of Simulation Parameters," Computational Economics, Springer;Society for Computational Economics, vol. 28(4), pages 371-397, November.
    17. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen W., 2018. "Robustness to strategic uncertainty in the Nash demand game," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 1-5.
    18. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    19. Yoshio Kamijo & Koji Yokote, 2022. "Behavioral bargaining theory: Equality bias, risk attitude, and reference-dependent utility," Working Papers 2208, Waseda University, Faculty of Political Science and Economics.
    20. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.
    21. Heinrich H. Nax & Bary S. R. Pradelski, 2016. "Core Stability and Core Selection in a Decentralized Labor Matching Market," Games, MDPI, vol. 7(2), pages 1-16, March.

    More about this item

    Keywords

    bargaining; evolution; stable behavioural rules; internal stability; external stability; equal split;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:90811. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.