IDEAS home Printed from https://ideas.repec.org/a/wly/econjl/v118y2008i532p1719-1741.html
   My bibliography  Save this article

Mistakes in Cooperation: The Stochastic Stability of Edgeworth's Recontracting

Author

Listed:
  • Roberto Serrano
  • Oscar Volij

Abstract

We analyse a dynamic trading process of coalitional recontracting in an exchange economy with indivisible goods, where agents may make mistakes with small probability. According to this process, the resistance of a transition from one allocation to another is a function of the number of agents who make mistakes and of the seriousness of each mistake. If preferences are always strict, the unique stochastically stable state is the competitive equilibrium allocation. In economies with indifferences, non‐core cycles are sometimes stochastically stable, while some core allocations are not. The robustness of these results is confirmed in a weak coalitional recontracting process.

Suggested Citation

  • Roberto Serrano & Oscar Volij, 2008. "Mistakes in Cooperation: The Stochastic Stability of Edgeworth's Recontracting," Economic Journal, Royal Economic Society, vol. 118(532), pages 1719-1741, October.
  • Handle: RePEc:wly:econjl:v:118:y:2008:i:532:p:1719-1741
    DOI: 10.1111/j.1468-0297.2008.02187.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1468-0297.2008.02187.x
    Download Restriction: no

    File URL: https://libkey.io/10.1111/j.1468-0297.2008.02187.x?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Perry, Motty & Reny, Philip J, 1994. "A Noncooperative View of Coalition Formation and the Core," Econometrica, Econometric Society, vol. 62(4), pages 795-817, July.
    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. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 457-488.
    4. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    5. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    6. Feldman, Allan M, 1974. "Recontracting Stability," Econometrica, Econometric Society, vol. 42(1), pages 35-44, January.
    7. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-138, January.
    8. Green, Jerry R, 1974. "The Stability of Edgeworth's Recontracting Process," Econometrica, Econometric Society, vol. 42(1), pages 21-34, January.
    9. Debraj Ray & Rajiv Vohra, 2001. "Coalitional Power and Public Goods," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1355-1384, December.
    10. Kandori, Michihiro & Serrano, Roberto & Volij, Oscar, 2008. "Decentralized trade, random utility and the evolution of social welfare," Journal of Economic Theory, Elsevier, vol. 140(1), pages 328-338, May.
    11. Roberto Serrano & Rajiv Vohra & Oscar Volij, 2001. "On the Failure of Core Convergence in Economies with Asymmetric Information," Econometrica, Econometric Society, vol. 69(6), pages 1685-1696, November.
    12. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    13. Nir Dagan & Roberto Serrano & Oscar Volij, 2000. "Bargaining, coalitions and competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 279-296, March.
    14. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
    15. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    16. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    17. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    18. Robert M. Anderson & William R. Zame, 1997. "Edgeworth's Conjecture with Infinitely Many Commodities: L1," Econometrica, Econometric Society, vol. 65(2), pages 225-274, March.
    19. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457, Elsevier.
    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. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    22. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    23. Ben-Shoham, Assaf & Serrano, Roberto & Volij, Oscar, 2004. "The evolution of exchange," Journal of Economic Theory, Elsevier, vol. 114(2), pages 310-328, February.
    24. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    25. Assaf Ben-Shoham & Roberto Serrano & Oscar Volig, 2000. "The Evolution of Change," Working Papers 2000-06, Brown University, Department of Economics.
    26. Volij, Oscar & Serano, Roberto & Vohra, Rajiv, 2001. "On the Failure of Core Convergence," Staff General Research Papers Archive 5098, Iowa State University, Department of Economics.
    27. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    28. Edgeworth, Francis Ysidro, 1881. "Mathematical Psychics," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number edgeworth1881.
    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. Kamijo, Yoshio & Kawasaki, Ryo, 2010. "Dynamics, stability, and foresight in the Shapley-Scarf housing market," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 214-222, March.
    2. Mandel, Antoine & Gintis, Herbert, 2016. "Decentralized Pricing and the equivalence between Nash and Walrasian equilibrium," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 84-92.
    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. Zhiwei Cui & Yan-An Hwang, 2017. "House exchange and residential segregation in networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 125-147, March.
    5. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
    6. Newton, Jonathan, 2015. "Stochastic stability on general state spaces," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 46-60.
    7. Kandori, Michihiro & Serrano, Roberto & Volij, Oscar, 2008. "Decentralized trade, random utility and the evolution of social welfare," Journal of Economic Theory, Elsevier, vol. 140(1), pages 328-338, May.
    8. Tatur, Tymon, 2023. "Evolutionarily rational mutations in structured populations," Journal of Economic Theory, Elsevier, vol. 212(C).
    9. Klaus, Bettina & Bochet, Olivier & Walzl, Markus, 2011. "A dynamic recontracting process for multiple-type housing markets," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 84-98, January.
    10. Klaus, Bettina & Newton, Jonathan, 2016. "Stochastic stability in assignment problems," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 62-74.
    11. Roland Pongou & Roberto Serrano, 2009. "A dynamic theory of fidelity networks with an application to the spread of HIV/AIDS," Working Papers 2009-03, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    12. Mandel Antoine & Botta Nicola, 2009. "A Note on Herbert Gintis' "Emergence of a Price System from Decentralized Bilateral Exchange"," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-18, December.
    13. 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.
    14. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    15. Kawasaki, Ryo, 2010. "Farsighted stability of the competitive allocations in an exchange economy with indivisible goods," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 46-52, January.
    16. Mandel, Antoine & Gintis, Herbert, 2014. "Stochastic stability in the Scarf economy," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 44-49.
    17. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Farsighted house allocation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 817-824, September.
    18. 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.
    19. Afacan, Mustafa Oğuz & Hu, Gaoji & Li, Jiangtao, 2024. "Housing markets since Shapley and Scarf," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    20. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    21. repec:hal:pseose:halshs-01296646 is not listed on IDEAS
    22. Kawasaki, Ryo, 2015. "Roth–Postlewaite stability and von Neumann–Morgenstern stability," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 1-6.

    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, vol. 9(2), pages 1-67, May.
    2. 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.
    3. Committee, Nobel Prize, 2012. "Alvin E. Roth and Lloyd S. Shapley: Stable allocations and the practice of market design," Nobel Prize in Economics documents 2012-1, Nobel Prize Committee.
    4. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.
    5. Sawa, Ryoji, 2019. "Stochastic stability under logit choice in coalitional bargaining problems," Games and Economic Behavior, Elsevier, vol. 113(C), pages 633-650.
    6. Zhiwei Cui & Yan-An Hwang, 2017. "House exchange and residential segregation in networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 125-147, March.
    7. Roland Pongou & Roberto Serrano, 2009. "A dynamic theory of fidelity networks with an application to the spread of HIV/AIDS," Working Papers 2009-03, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    8. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Kandori, Michihiro & Serrano, Roberto & Volij, Oscar, 2008. "Decentralized trade, random utility and the evolution of social welfare," Journal of Economic Theory, Elsevier, vol. 140(1), pages 328-338, May.
    10. BOCHET, Olivier & KLAUS, Bettina & WALZL, Markus, 2007. "Dynamic recontracting processes with multiple indivisible goods," LIDAM Discussion Papers CORE 2007061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
    12. Chongmin Kim & Kam-Chau Wong, 2011. "Evolution of Walrasian equilibrium in an exchange economy," Journal of Evolutionary Economics, Springer, vol. 21(4), pages 619-647, October.
    13. Leonardo Boncinelli & Alessio Muscillo & Paolo Pin, 2022. "Efficiency and Stability in a Process of Teams Formation," Dynamic Games and Applications, Springer, vol. 12(4), pages 1101-1129, December.
    14. Ben-Shoham, Assaf & Serrano, Roberto & Volij, Oscar, 2004. "The evolution of exchange," Journal of Economic Theory, Elsevier, vol. 114(2), pages 310-328, February.
    15. Klaus, Bettina & Bochet, Olivier & Walzl, Markus, 2011. "A dynamic recontracting process for multiple-type housing markets," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 84-98, January.
    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. Demuynck, Thomas & Herings, P. Jean-Jacques & Saulle, Riccardo & Seel, Christian, 2018. "The Myopic Stable Set for Social Environments (RM/17/002-revised)," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    18. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
    19. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    20. Oscar Volij, 1998. "In Defense of DEFECT or Cooperation does not Justify the Solution Concept," Economic theory and game theory 007, Oscar Volij, revised 26 Aug 1999.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    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:wly:econjl:v:118:y:2008:i:532:p:1719-1741. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/resssea.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.