IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/9811003.html
   My bibliography  Save this paper

Stability of Equilibria in Games with Procedurally Rational Players

Author

Listed:
  • Rajiv Sethi

    (Barnard College, Columbia University)

Abstract

One approach to the modeling of bounded rationality in strategic environments is based on the dynamics of evolution and learning in games. An entirely different approach has been developed recently by Osborne and Rubinstein (1998). This latter approach is static and equilibrium based, but relies on less stringent assumptions regarding the knowledge and understanding of players than does the standard theory of Nash equilibrium. This paper formalizes Osborne and Rubinstein's dynamic interpretation of their equilibrium concept and thereby facilitates a comparison of this approach with the explicitly dynamic approach of evolutionary game theory. It turns out that the two approaches give rise to radically different static and dynamic predictions. For instance, dynamically stable equilibria can involve the playing of strictly dominated actions, and equilibria in which strictly actions are played with probability 1 can be unstable. Sufficient conditions for the instability of equilibria are provided for symmetric and asymmetric games.

Suggested Citation

  • Rajiv Sethi, 1998. "Stability of Equilibria in Games with Procedurally Rational Players," Game Theory and Information 9811003, University Library of Munich, Germany, revised 04 Mar 1999.
  • Handle: RePEc:wpa:wuwpga:9811003
    Note: Type of Document - Tex; prepared on IBM PC; to print on HP/PostScript; pages: 23; figures: included
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9811/9811003.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    2. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
    3. Simon, Herbert A, 1978. "Rationality as Process and as Product of Thought," American Economic Review, American Economic Association, vol. 68(2), pages 1-16, May.
    4. Sethi, Rajiv, 1998. "Strategy-Specific Barriers to Learning and Nonmonotonic Selection Dynamics," Games and Economic Behavior, Elsevier, vol. 23(2), pages 284-304, May.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. Dekel, Eddie & Scotchmer, Suzanne, 1992. "On the evolution of optimizing behavior," Journal of Economic Theory, Elsevier, vol. 57(2), pages 392-406, August.
    7. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    8. 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.
    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. Huck Steffen & Sarin Rajiv, 2004. "Players With Limited Memory," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 4(1), pages 1-27, September.
    2. Juan Camilo Cárdenas & César Mantilla & Rajiv Sethi, 2015. "Stable Sampling Equilibrium in Common Pool Resource Games," Games, MDPI, vol. 6(3), pages 1-19, August.
    3. Srinivas Arigapudi & Omer Edhan & Yuval Heller & Ziv Hellman, 2022. "Mentors and Recombinators: Multi-Dimensional Social Learning," Papers 2205.00278, arXiv.org.
    4. Cárdenas, Juan-Camilo & Gómez, Santiago & Mantilla, César, 2019. "Between-group competition enhances cooperation in resource appropriation games," Ecological Economics, Elsevier, vol. 157(C), pages 17-26.
    5. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2020. "Stability for best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 185(C).
    6. Robert Rowthorn & Rajiv Sethi, 2008. "Procedural Rationality and Equilibrium Trust," Economic Journal, Royal Economic Society, vol. 118(530), pages 889-905, July.
    7. Jacek Miękisz & Michał Ramsza, 2013. "Sampling Dynamics of a Symmetric Ultimatum Game," Dynamic Games and Applications, Springer, vol. 3(3), pages 374-386, September.
    8. Oechssler, Jorg & Schipper, Burkhard, 2003. "Can you guess the game you are playing?," Games and Economic Behavior, Elsevier, vol. 43(1), pages 137-152, April.
    9. Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2020. "Instability of Defection in the Prisoner’s Dilemma: Best Experienced Payoff Dynamics Analysis," MPRA Paper 99594, University Library of Munich, Germany.
    10. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2019. "Best experienced payoff dynamics and cooperation in the Centipede game," Theoretical Economics, Econometric Society, vol. 14(4), November.
    11. Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2021. "Instability of defection in the prisoner's dilemma under best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 197(C).
    12. Yuval Salant & Josh Cherry, 2020. "Statistical Inference in Games," Econometrica, Econometric Society, vol. 88(4), pages 1725-1752, July.
    13. Ryoji Sawa, 2022. "Statistical Inference in Evolutionary Dynamics," Working Papers e170, Tokyo Center for Economic Research.
    14. Shahi, Chander & Kant, Shashi, 2007. "An evolutionary game-theoretic approach to the strategies of community members under Joint Forest Management regime," Forest Policy and Economics, Elsevier, vol. 9(7), pages 763-775, April.
    15. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2021. "Sampling dynamics and stable mixing in hawk-dove games," Papers 2107.08423, arXiv.org, revised Jun 2022.
    16. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    17. Thorsten Chmura & Werner Güth, 2011. "The Minority of Three-Game: An Experimental and Theoretical Analysis," Games, MDPI, vol. 2(3), pages 1-22, September.
    18. Sethi, Rajiv, 2021. "Stable sampling in repeated games," Journal of Economic Theory, Elsevier, vol. 197(C).
    19. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    20. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    21. Arigapudi, Srinivas & Heller, Yuval & Schreiber, Amnon, 2021. "Sampling Dynamics and Stable Mixing in Hawk–Dove Games," MPRA Paper 108819, University Library of Munich, Germany.
    22. J. C. R. Alcantud & Carlos Alós-Ferrer, 2002. "Choice-Nash Equilibria," Vienna Economics Papers 0209, University of Vienna, Department of Economics.
    23. Srinivas Arigapudi & Yuval Heller & Igal Milchtaich, 2020. "Instability of Defection in the Prisoner's Dilemma Under Best Experienced Payoff Dynamics," Papers 2005.05779, arXiv.org, revised Jan 2021.
    24. Juan Camilo Cárdenas & César Mantilla & Rajiv Sethi, 2013. "Commons without Tragedy: Sampling Dynamics and Cooperative Resource Extraction," Documentos CEDE 011892, Universidad de los Andes – Facultad de Economía – CEDE.

    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. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    3. Norman, Thomas W.L., 2009. "Rapid evolution under inertia," Games and Economic Behavior, Elsevier, vol. 66(2), pages 865-879, July.
    4. Ellison, Glenn, 1997. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Games and Economic Behavior, Elsevier, vol. 19(2), pages 180-210, May.
    5. Gerard van der Laan & A.F. Tieman, 1996. "Evolutionary Game Theory and the Modelling of Economic Behavior," Tinbergen Institute Discussion Papers 96-172/8, Tinbergen Institute.
    6. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    7. Jean-Paul Carvalho, 2017. "Coordination and culture," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 449-475, October.
    8. Neary, Philip R., 2012. "Competing conventions," Games and Economic Behavior, Elsevier, vol. 76(1), pages 301-328.
    9. 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.
    10. Jonathan Bendor & Piotr Swistak, 1998. "Evolutionary Equilibria: Characterization Theorems and Their Implications," Theory and Decision, Springer, vol. 45(2), pages 99-159, October.
    11. 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.
    12. 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.
    13. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
    14. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    15. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    16. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    17. Sanjeev Goyal & Fernando Vega-Redondo, 2000. "Learning, Network Formation and Coordination," Econometric Society World Congress 2000 Contributed Papers 0113, Econometric Society.
    18. Conley, John P. & Neilson, William S., 2013. "Endogenous coordination and discoordination games: Multiculturalism and assimilation," Journal of Economic Behavior & Organization, Elsevier, vol. 92(C), pages 176-191.
    19. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    20. Fernando Vega Redondo, 1993. "On The Evolution Of Cooperation In General Games Of Common Interest," Working Papers. Serie AD 1993-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

    More about this item

    Keywords

    Dynamic Stability; S(1) Equilibrium; Procedural Rationality; Evolutionary Games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wpa:wuwpga:9811003. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.