IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v62y2007i4p311-333.html
   My bibliography  Save this article

Stochastic Evolution of Rules for Playing Finite Normal Form Games

Author

Listed:
  • Fabrizio Germano

Abstract

The evolution of boundedly rational rules for playing normal form games is studied within stationary environments of stochastically changing games. Rules are viewed as algorithms prescribing strategies for the different normal form games that arise. It is shown that many of the “folk resultsâ€\x9D of evolutionary game theory, typically obtained with a fixed game and fixed strategies, carry over to the present environments. The results are also related to some recent experiments on rules and games. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May.
    • Handle: RePEc:kap:theord:v:62:y:2007:i:4:p:311-333
    DOI: 10.1007/s11238-007-9032-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11238-007-9032-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-007-9032-8?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. Viossat, Yannick, 2007. "The replicator dynamics does not lead to correlated equilibria," Games and Economic Behavior, Elsevier, vol. 59(2), pages 397-407, May.
    2. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    3. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    4. 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.
    5. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    6. Sergiu Hart & Andreu Mas-Colell, 2013. "A General Class Of Adaptive Strategies," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 3, pages 47-76, World Scientific Publishing Co. Pte. Ltd..
    7. Selten, Reinhard & Abbink, Klaus & Buchta, Joachim & Sadrieh, Abdolkarim, 2003. "How to play (3 x 3)-games.: A strategy method experiment," Games and Economic Behavior, Elsevier, vol. 45(1), pages 19-37, October.
    8. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    9. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    10. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    11. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    12. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
    13. Heller, Dana, 2004. "An evolutionary approach to learning in a changing environment," Journal of Economic Theory, Elsevier, vol. 114(1), pages 31-55, January.
    14. Cabrales, Antonio, 2000. "Stochastic Replicator Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-481, May.
    15. Dale O. Stahl, 1999. "Evidence based rules and learning in symmetric normal-form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 111-130.
    16. Cabrales, Antonio & Sobel, Joel, 1992. "On the limit points of discrete selection dynamics," Journal of Economic Theory, Elsevier, vol. 57(2), pages 407-419, August.
    17. 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.
    18. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
    19. D. Sgroi & D. J. Zizzo, 2002. "Strategy Learning in 3x3 Games by Neural Networks," Cambridge Working Papers in Economics 0207, Faculty of Economics, University of Cambridge.
    20. Daniel John Zizzo & Daniel Sgroi, 2001. "Bounded-Rational Behavior by Neural Networks in Normal Form Games," Economics Series Working Papers 2000-W30, University of Oxford, Department of Economics.
    21. Fabrizio Germano, 2004. "Stochastic evolution of rules for playing normal form games," Economics Working Papers 761, Department of Economics and Business, Universitat Pompeu Fabra.
    22. Rosenthal, R W, 1979. "Sequences of Games with Varying Opponents," Econometrica, Econometric Society, vol. 47(6), pages 1353-1366, November.
    23. Sergiu Hart & Andreu Mas-Colell, 2013. "Regret-Based Continuous-Time Dynamics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 5, pages 99-124, World Scientific Publishing Co. Pte. Ltd..
    24. LiCalzi Marco, 1995. "Fictitious Play by Cases," Games and Economic Behavior, Elsevier, vol. 11(1), pages 64-89, October.
    25. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    26. 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..
    27. Stahl, Dale O., 2000. "Rule Learning in Symmetric Normal-Form Games: Theory and Evidence," Games and Economic Behavior, Elsevier, vol. 32(1), pages 105-138, July.
    28. Rankin, Frederick W. & Van Huyck, John B. & Battalio, Raymond C., 2000. "Strategic Similarity and Emergent Conventions: Evidence from Similar Stag Hunt Games," Games and Economic Behavior, Elsevier, vol. 32(2), pages 315-337, August.
    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. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    2. Terje Lensberg & Klaus Reiner Schenk-Hoppe, 2019. "Evolutionary Stable Solution Concepts for the Initial Play," Economics Discussion Paper Series 1916, Economics, The University of Manchester.
    3. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    4. Lensberg, Terje & Schenk-Hoppé, Klaus Reiner, 2021. "Cold play: Learning across bimatrix games," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 419-441.
    5. Rabah Amir & Igor Evstigneev & Klaus Schenk-Hoppé, 2013. "Asset market games of survival: a synthesis of evolutionary and dynamic games," Annals of Finance, Springer, vol. 9(2), pages 121-144, May.
    6. Spiliopoulos, Leonidas, 2009. "Neural networks as a learning paradigm for general normal form games," MPRA Paper 16765, University Library of Munich, Germany.
    7. Schipper, Burkhard C., 2008. "On An Evolutionary Foundation Of Neuroeconomics," Economics and Philosophy, Cambridge University Press, vol. 24(3), pages 495-513, November.
    8. Rabah Amir & Igor V. Evstigneev & Valeriya Potapova, 2021. "Unbeatable Strategies," Economics Discussion Paper Series 2101, Economics, The University of Manchester, revised Jul 2023.
    9. Sergei Belkov & Igor V. Evstigneev & Thorsten Hens, 2020. "An evolutionary finance model with a risk-free asset," Annals of Finance, Springer, vol. 16(4), pages 593-607, December.
    10. Spiliopoulos, Leonidas, 2012. "Interactive learning in 2×2 normal form games by neural network agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5557-5562.
    11. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.
    12. Lars P. Metzger, 2018. "Evolution and correlated equilibrium," Journal of Evolutionary Economics, Springer, vol. 28(2), pages 333-346, April.
    13. Schipper, Burkhard C., 2008. "On An Evolutionary Foundation Of Neuroeconomics," Economics and Philosophy, Cambridge University Press, vol. 24(03), pages 495-513, November.

    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. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    2. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
    3. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    4. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
    5. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    6. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
    7. Reinoud Joosten & Berend Roorda, 2008. "Generalized projection dynamics in evolutionary game theory," Papers on Economics and Evolution 2008-11, Philipps University Marburg, Department of Geography.
    8. Haruvy, Ernan & Stahl, Dale O., 2012. "Between-game rule learning in dissimilar symmetric normal-form games," Games and Economic Behavior, Elsevier, vol. 74(1), pages 208-221.
    9. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    11. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    12. Yannick Viossat, 2015. "Evolutionary dynamics and dominated strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 91-113, April.
    13. Teck-Hua Ho & So-Eun Park & Xuanming Su, 2021. "A Bayesian Level- k Model in n -Person Games," Management Science, INFORMS, vol. 67(3), pages 1622-1638, March.
    14. Rick, Scott & Weber, Roberto A., 2010. "Meaningful learning and transfer of learning in games played repeatedly without feedback," Games and Economic Behavior, Elsevier, vol. 68(2), pages 716-730, March.
    15. Wolf Ze'ev Ehrblatt & Kyle Hyndman & Erkut Y. ÄOzbay & Andrew Schotter, 2006. "Convergence: An Experimental Study," Levine's Working Paper Archive 122247000000001148, David K. Levine.
    16. Battalio,R. & Samuelson,L. & Huyck,J. van, 1998. "Risk dominance, payoff dominance and probabilistic choice learning," Working papers 2, Wisconsin Madison - Social Systems.
    17. Berger, Ulrich & Hofbauer, Josef, 2006. "Irrational behavior in the Brown-von Neumann-Nash dynamics," Games and Economic Behavior, Elsevier, vol. 56(1), pages 1-6, July.
    18. Chernov, G. & Susin, I., 2019. "Models of learning in games: An overview," Journal of the New Economic Association, New Economic Association, vol. 44(4), pages 77-125.
    19. Panayotis Mertikopoulos & William H. Sandholm, 2016. "Learning in Games via Reinforcement and Regularization," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1297-1324, November.
    20. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 147-161, October.

    More about this item

    Keywords

    bounded rationality; evolutionary dynamics; learning; normal form games; rules; stochastic dynamics; C72; C73; D81; D83;
    All these keywords.

    JEL classification:

    • 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
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:kap:theord:v:62:y:2007:i:4:p:311-333. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.