IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v134y2022icp361-375.html
   My bibliography  Save this article

Convergence of incentive-driven dynamics in Fisher markets

Author

Listed:
  • Dvijotham, Krishnamurthy
  • Rabani, Yuval
  • Schulman, Leonard J.

Abstract

We study out-of-equilibrium price dynamics in Fisher markets. We develop a general framework in which sellers have (a) a set of atomic price update rules (APU), which are simple responses to a price vector; (b) a belief-formation procedure that simulates actions of other sellers (themselves using the APU) to some finite horizon in the future. Sellers use an APU to respond to a price vector they generate with the belief formation procedure. The framework allows sellers to have inconsistent and time-varying beliefs about each other. Under mild and natural assumptions on the APU, we show that despite the inconsistent and time-varying nature of beliefs, the market converges to a unique equilibrium at a linear rate (distance to equilibrium decreases exponentially in time). If the APU are driven by weak gross substitutes demands, the equilibrium point is the same as predicted by those demands.

Suggested Citation

  • Dvijotham, Krishnamurthy & Rabani, Yuval & Schulman, Leonard J., 2022. "Convergence of incentive-driven dynamics in Fisher markets," Games and Economic Behavior, Elsevier, vol. 134(C), pages 361-375.
  • Handle: RePEc:eee:gamebe:v:134:y:2022:i:c:p:361-375
    DOI: 10.1016/j.geb.2020.11.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825620301585
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.geb.2020.11.005?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. Borgs, Christian & Chayes, Jennifer & Immorlica, Nicole & Kalai, Adam Tauman & Mirrokni, Vahab & Papadimitriou, Christos, 2010. "The myth of the Folk Theorem," Games and Economic Behavior, Elsevier, vol. 70(1), pages 34-43, September.
    2. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    3. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    4. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
    5. Chien, Steve & Sinclair, Alistair, 2011. "Convergence to approximate Nash equilibria in congestion games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 315-327, March.
    6. Vincent P. Crawford & Nagore Iriberri, 2007. "Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," Econometrica, Econometric Society, vol. 75(6), pages 1721-1770, November.
    7. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    8. Terri Kneeland, 2015. "Identifying Higher‐Order Rationality," Econometrica, Econometric Society, vol. 83(5), pages 2065-2079, September.
    9. Olga Gorelkina, 2018. "The expected externality mechanism in a level-k environment," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 103-131, March.
    10. Mukherji, Anjan, 2002. "An Introduction to General Equilibrium Analysis: Walrasian and Non-Walrasian Equilibria," OUP Catalogue, Oxford University Press, number 9780195659078, Decembrie.
    11. Vincent P. Crawford & Nagore Iriberri, 2007. "Fatal Attraction: Salience, Naïveté, and Sophistication in Experimental "Hide-and-Seek" Games," American Economic Review, American Economic Association, vol. 97(5), pages 1731-1750, December.
    12. Ho, Teck-Hua & Camerer, Colin & Weigelt, Keith, 1998. "Iterated Dominance and Iterated Best Response in Experimental "p-Beauty Contests."," American Economic Review, American Economic Association, vol. 88(4), pages 947-969, September.
    13. Vincent P. Crawford & Nagore Iriberri, 2007. "Fatal Attraction: Salience, Naïveté, and Sophistication in Experimental "Hide-and-Seek" Games," American Economic Review, American Economic Association, vol. 97(5), pages 1731-1750, December.
    14. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    15. Vincent P. Crawford, 2003. "Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions," American Economic Review, American Economic Association, vol. 93(1), pages 133-149, March.
    16. Geoffroy de Clippel & Rene Saran & Roberto Serrano, 2014. "Mechanism Design with Bounded Depth of Reasoning and Small Modeling Mistakes," Working Papers 2014-7, Brown University, Department of Economics.
    17. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2013. "Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications," Journal of Economic Literature, American Economic Association, vol. 51(1), pages 5-62, March.
    18. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
    19. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    20. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    21. Jain, Kamal & Vazirani, Vijay V., 2010. "Eisenberg-Gale markets: Algorithms and game-theoretic properties," Games and Economic Behavior, Elsevier, vol. 70(1), pages 84-106, September.
    22. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
    23. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    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. Yoav Kolumbus & Menahem Levy & Noam Nisan, 2023. "Asynchronous Proportional Response Dynamics in Markets with Adversarial Scheduling," Papers 2307.04108, arXiv.org, revised Jan 2024.

    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. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
    2. Kneeland, Terri, 2022. "Mechanism design with level-k types: Theory and an application to bilateral trade," Journal of Economic Theory, Elsevier, vol. 201(C).
    3. Georganas, Sotiris & Healy, Paul J. & Weber, Roberto A., 2015. "On the persistence of strategic sophistication," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 369-400.
    4. Dengler, Sebastian & Prüfer, Jens, 2021. "Consumers' privacy choices in the era of big data," Games and Economic Behavior, Elsevier, vol. 130(C), pages 499-520.
    5. Alaoui, Larbi & Janezic, Katharina A. & Penta, Antonio, 2020. "Reasoning about others' reasoning," Journal of Economic Theory, Elsevier, vol. 189(C).
    6. Binswanger, Johannes & Prüfer, Jens, 2012. "Democracy, populism, and (un)bounded rationality," European Journal of Political Economy, Elsevier, vol. 28(3), pages 358-372.
    7. Berger, Ulrich & De Silva, Hannelore & Fellner-Röhling, Gerlinde, 2016. "Cognitive hierarchies in the minimizer game," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 337-348.
    8. Kneeland, Terri, 2017. "Mechanism design with level-k types: Theory and an application to bilateral trade," Discussion Papers, Research Unit: Economics of Change SP II 2017-303, WZB Berlin Social Science Center.
    9. Crawford, Vincent P., 2017. "Let׳s talk it over: Coordination via preplay communication with level-k thinking," Research in Economics, Elsevier, vol. 71(1), pages 20-31.
    10. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
    11. Arad Ayala, 2012. "The Tennis Coach Problem: A Game-Theoretic and Experimental Study," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-43, April.
    12. Giovanna Devetag & Sibilla Guida & Luca Polonio, 2016. "An eye-tracking study of feature-based choice in one-shot games," Experimental Economics, Springer;Economic Science Association, vol. 19(1), pages 177-201, March.
    13. Dufwenberg, Martin & Sundaram, Ramya & Butler, David J., 2010. "Epiphany in the Game of 21," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 132-143, August.
    14. Dugar, Subhasish & Shahriar, Quazi, 2023. "Lying for votes," Games and Economic Behavior, Elsevier, vol. 142(C), pages 46-72.
    15. Jin, Ye, 2022. "Reinvestigating Rk behavior in ring games," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 98(C).
    16. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    17. Shapiro, Dmitry & Shi, Xianwen & Zillante, Artie, 2014. "Level-k reasoning in a generalized beauty contest," Games and Economic Behavior, Elsevier, vol. 86(C), pages 308-329.
    18. Wright, James R. & Leyton-Brown, Kevin, 2017. "Predicting human behavior in unrepeated, simultaneous-move games," Games and Economic Behavior, Elsevier, vol. 106(C), pages 16-37.
    19. Tong, Hanh T. & Freeman, David J., 2021. "Anchors of strategic reasoning in the traveler’s dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 28-38.
    20. Arad, Ayala, 2008. "The Tennis Coach Problem: A Game-Theoretic and Experimental Study," Foerder Institute for Economic Research Working Papers 275711, Tel-Aviv University > Foerder Institute for Economic Research.

    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:134:y:2022:i:c:p:361-375. 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: 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. RePEc uses bibliographic data supplied by the respective publishers.