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Bargaining and Markets: Complexity and the Walrasian Outcome


  • Hamid Sabourian

    (King's College, Cambridge, UK)


Rubinstein and Wolinsky (1990b) consider a simple decentralized market in which agents either meet randomly or choose their partners volunatarily and bargain over the terms on which they are willing to trade. Intuition suggests that if there are no transaction costs, the outcome of this matching and bargaining game should be the unique competitive equilibrium. This does not happen. In fact, Rubinstein and Wolinsky show that any price can be sustained as a sequential equilibrium of this game. In this paper, I consider Rubinstein and Wolinsky's model and show that if the complexity costs of implementing strategies enter players' preferences (lexicographically), together with the standard payoff in the game, then the only equilibrium that survives is the unique competitive outcome. This will be done both for the random matching and for the voluntary matching models. Thus the paper demonstrates that complexity costs might have a role in providing a justification for the competitive outcome.

Suggested Citation

  • Hamid Sabourian, 2000. "Bargaining and Markets: Complexity and the Walrasian Outcome," Cowles Foundation Discussion Papers 1249, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1249

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    References listed on IDEAS

    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Gale,Douglas, 2000. "Strategic Foundations of General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521644105, March.
    3. Piccione Michele & Rubinstein Ariel, 1993. "Finite Automata Play a Repeated Extensive Game," Journal of Economic Theory, Elsevier, vol. 61(1), pages 160-168, October.
    4. Kalai, E & Neme, A, 1992. "The Strength of a Little Perfection," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 335-355.
    5. 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..
    6. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
    7. Levine, David K & Pesendorfer, Wolfgang, 1995. "When Are Agents Negligible?," American Economic Review, American Economic Association, vol. 85(5), pages 1160-1170, December.
    8. Green, Edward J., 1980. "Noncooperative price taking in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 22(2), pages 155-182, April.
    9. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    10. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
    11. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
    12. Binmore, K. & Piccione, M. & Samuelson, L., 1996. "Evolutionary Stability in Alternating-Offers Bargaining Games," Working papers 9603r, Wisconsin Madison - Social Systems.
    13. Binmore, Ken & Piccione, Michele & Samuelson, Larry, 1998. "Evolutionary Stability in Alternating-Offers Bargaining Games," Journal of Economic Theory, Elsevier, vol. 80(2), pages 257-291, June.
    14. K. G. Binmore & M. J. Herrero, 1988. "Matching and Bargaining in Dynamic Markets," Review of Economic Studies, Oxford University Press, vol. 55(1), pages 17-31.
    15. Gale, Douglas M, 1986. "Bargaining and Competition Part I: Characterization," Econometrica, Econometric Society, vol. 54(4), pages 785-806, July.
    16. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    17. Ariel Rubinstein & Asher Wolinsky, 1990. "Decentralized Trading, Strategic Behaviour and the Walrasian Outcome," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 63-78.
    18. Piccione, M. & Rubinstein, A., 1992. "Finite Automata Play A Repeated Extensive Game," Papers 5-92, Tel Aviv.
    19. McLennan, Andrew & Sonnenschein, Hugo, 1991. "Sequential Bargaining as a Noncooperative Foundation for Walrasian Equilibrium," Econometrica, Econometric Society, vol. 59(5), pages 1395-1424, September.
    20. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
    21. Ehud Kalai, 1987. "Bounded Rationality and Strategic Complexity in Repeated Games," Discussion Papers 783, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    22. Sabourian, Hamid, 1990. "Anonymous repeated games with a large number of players and random outcomes," Journal of Economic Theory, Elsevier, vol. 51(1), pages 92-110, June.
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    Cited by:

    1. Gale, D. & Sabourian, H., 2003. "Complexity and Competition, Part I: Sequential Matching," Cambridge Working Papers in Economics 0345, Faculty of Economics, University of Cambridge.
    2. repec:spr:grdene:v:11:y:2002:i:3:d:10.1023_a:1015236512713 is not listed on IDEAS
    3. Penta, Antonio, 2011. "Multilateral bargaining and Walrasian equilibrium," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 417-424.
    4. Maenner, Eliot, 2008. "Adaptation and complexity in repeated games," Games and Economic Behavior, Elsevier, vol. 63(1), pages 166-187, May.

    More about this item


    Bargaining; matching; complexity; automata; bounded rationality; competitive outcome; Walrasian equilibrium;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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