IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v113y2019icp633-650.html
   My bibliography  Save this article

Stochastic stability under logit choice in coalitional bargaining problems

Author

Listed:
  • Sawa, Ryoji

Abstract

This study examines a dynamic process of n-person coalitional bargaining problems. We investigate the evolution of social conventions by embedding a coalitional bargaining setting in a dynamic process. In each period, a group of players may make some coalitional move, that is, forming a new team or negotiating the division of a surplus. Players revise their coalitions and surplus divisions over time in the presence of stochastic noise, which leads players to make a suboptimal decision. Under a logit specification of choice probabilities, we find that the stability of a core allocation decreases in the wealth of the richest player. Furthermore, stochastically stable allocations are core allocations that minimize the wealth of the richest player.

Suggested Citation

  • Sawa, Ryoji, 2019. "Stochastic stability under logit choice in coalitional bargaining problems," Games and Economic Behavior, Elsevier, vol. 113(C), pages 633-650.
  • Handle: RePEc:eee:gamebe:v:113:y:2019:i:c:p:633-650
    DOI: 10.1016/j.geb.2018.11.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825618301842
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.geb.2018.11.009?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. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    2. Armando Gomes & Philippe Jehiel, 2005. "Dynamic Processes of Social and Economic Interactions: On the Persistence of Inefficiencies," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 626-667, June.
    3. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    4. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, Open Access Journal, vol. 9(2), pages 1-67, May.
    5. repec:gam:jgames:v:7:y:2016:i:2:p:10:d:66888 is not listed on IDEAS
    6. Murali Agastya, 1997. "Adaptive Play in Multiplayer Bargaining Situations," Review of Economic Studies, Oxford University Press, vol. 64(3), pages 411-426.
    7. Newton, Jonathan & Sawa, Ryoji, 2015. "A one-shot deviation principle for stability in matching problems," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1-27.
    8. Kalyan Chatterjee & Bhaskar Dutia & Debraj Ray & Kunal Sengupta, 2013. "A Noncooperative Theory of Coalitional Bargaining," World Scientific Book Chapters, in: Bargaining in the Shadow of the Market Selected Papers on Bilateral and Multilateral Bargaining, chapter 5, pages 97-111, World Scientific Publishing Co. Pte. Ltd..
    9. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    10. Klaus, Bettina & Newton, Jonathan, 2016. "Stochastic stability in assignment problems," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 62-74.
    11. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    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. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January.
    14. Rozen, Kareen, 2013. "Conflict leads to cooperation in demand bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 87(C), pages 35-42.
    15. Agastya, Murali, 1999. "Perturbed Adaptive Dynamics in Coalition Form Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 207-233, December.
    16. Olivier Compte & Philippe Jehiel, 2010. "The Coalitional Nash Bargaining Solution," Econometrica, Econometric Society, vol. 78(5), pages 1593-1623, September.
    17. 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.
    18. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January.
    19. Saez-Marti, Maria & Weibull, Jorgen W., 1999. "Clever Agents in Young's Evolutionary Bargaining Model," Journal of Economic Theory, Elsevier, vol. 86(2), pages 268-279, June.
    20. 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.
    21. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.
    22. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    23. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    24. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    25. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    26. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    27. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
    28. Heinrich H. Nax & Bary S. R. Pradelski, 2016. "Core Stability and Core Selection in a Decentralized Labor Matching Market," Games, MDPI, Open Access Journal, vol. 7(2), pages 1-16, March.
    29. Boncinelli, Leonardo & Pin, Paolo, 2018. "The stochastic stability of decentralized matching on a graph," Games and Economic Behavior, Elsevier, vol. 108(C), pages 239-244.
    30. 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.
    31. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
    32. Naidu, Suresh & Hwang, Sung-Ha & Bowles, Samuel, 2010. "Evolutionary bargaining with intentional idiosyncratic play," Economics Letters, Elsevier, vol. 109(1), pages 31-33, October.
    33. Arnold, Tone & Schwalbe, Ulrich, 2002. "Dynamic coalition formation and the core," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 363-380, November.
    34. Lim, Wooyoung & Neary, Philip R., 2016. "An experimental investigation of stochastic adjustment dynamics," Games and Economic Behavior, Elsevier, vol. 100(C), pages 208-219.
    35. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
    36. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," LSE Research Online Documents on Economics 65422, London School of Economics and Political Science, LSE Library.
    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. 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, 2021. "Evolutionary stability of behavioural rules in bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 187(C), pages 399-414.

    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. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, Open Access Journal, vol. 9(2), pages 1-67, May.
    2. 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.
    3. Bilancini, Ennio & Boncinelli, Leonardo & Newton, Jonathan, 2020. "Evolution and Rawlsian social choice in matching," Games and Economic Behavior, Elsevier, vol. 123(C), pages 68-80.
    4. Klaus, Bettina & Newton, Jonathan, 2016. "Stochastic stability in assignment problems," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 62-74.
    5. Ennio Bilancini & Leonardo Boncinelli, 2020. "The evolution of conventions under condition-dependent mistakes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 497-521, March.
    6. 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.
    7. repec:gam:jgames:v:7:y:2016:i:2:p:10:d:66888 is not listed on IDEAS
    8. Heinrich H. Nax & Bary S. R. Pradelski, 2016. "Core Stability and Core Selection in a Decentralized Labor Matching Market," Games, MDPI, Open Access Journal, vol. 7(2), pages 1-16, March.
    9. Sawa, Ryoji & Wu, Jiabin, 2018. "Reference-dependent preferences, super-dominance and stochastic stability," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 96-104.
    10. 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.
    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. Newton, Jonathan & Wait, Andrew & Angus, Simon D., 2019. "Watercooler chat, organizational structure and corporate culture," Games and Economic Behavior, Elsevier, vol. 118(C), pages 354-365.
    13. Newton, Jonathan & Sawa, Ryoji, 2015. "A one-shot deviation principle for stability in matching problems," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1-27.
    14. 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.
    15. Bilancini, Ennio & Boncinelli, Leonardo & Nax, Heinrich H., 2021. "What noise matters? Experimental evidence for stochastic deviations in social norms," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 90(C).
    16. 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.
    17. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
    18. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.
    19. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    20. Rozen, Kareen, 2013. "Conflict leads to cooperation in demand bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 87(C), pages 35-42.
    21. Newton, Jonathan & Angus, Simon D., 2015. "Coalitions, tipping points and the speed of evolution," Journal of Economic Theory, Elsevier, vol. 157(C), pages 172-187.

    More about this item

    Keywords

    Stochastic stability; Coalitional bargaining; Coalition; Logit-response dynamics; Bargaining;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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

    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:gamebe:v:113:y:2019:i:c:p:633-650. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.elsevier.com/locate/inca/622836 .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.