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Markets, correlation, and regret-matching

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  • Hart, Sergiu
  • Mas-Colell, Andreu

Abstract

Inspired by the existing work on correlated equilibria and regret-based dynamics in games, we carry out a first exploration of the links between equilibria and dynamics in (exchange) economies. The leading equilibrium concept is Walrasian equilibrium, and the dynamics (specifically, regret-matching dynamics) apply to trading games that fit the economic structure and whose pure Nash equilibria implement the Walrasian outcomes. Interestingly, in the case of quasilinear utilities (or “transferable utility”), all the concepts essentially coincide, and we get simple deterministic dynamics converging to Walrasian outcomes. Connections to sunspot equilibria are also studied.

Suggested Citation

  • Hart, Sergiu & Mas-Colell, Andreu, 2015. "Markets, correlation, and regret-matching," Games and Economic Behavior, Elsevier, vol. 93(C), pages 42-58.
  • Handle: RePEc:eee:gamebe:v:93:y:2015:i:c:p:42-58
    DOI: 10.1016/j.geb.2015.06.009
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    References listed on IDEAS

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    1. L. Hurwicz, 1979. "Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 217-225.
    2. Forges, Francoise & Peck, James, 1995. "Correlated Equilibrium and Sunspot Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 33-50, January.
    3. Hart, Sergiu & Mas-Colell, Andreu, 2003. "Regret-based continuous-time dynamics," Games and Economic Behavior, Elsevier, vol. 45(2), pages 375-394, November.
    4. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
    5. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    6. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    7. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
    8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    9. Polemarchakis, Herakles M. & Ray, Indrajit, 2006. "Sunspots, correlation and competition," Games and Economic Behavior, Elsevier, vol. 56(1), pages 174-184, July.
    10. Schmeidler, David, 1980. "Walrasian Analysis via Strategic Outcome Functions," Econometrica, Econometric Society, vol. 48(7), pages 1585-1593, November.
    11. Maskin, Eric & Tirole, Jean, 1987. "Correlated equilibria and sunspots," Journal of Economic Theory, Elsevier, vol. 43(2), pages 364-373, December.
    12. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
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    More about this item

    Keywords

    Exchange economies; Walrasian equilibrium; Correlated equilibrium; Sunspot equilibrium; Dynamics; Regret-matching; Socially concave games; Deterministic regret-matching dynamics; Hannan set; Implementation of Walrasian equilibria;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium

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