IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v197y2021ics0022053121001605.html
   My bibliography  Save this article

Stable sampling in repeated games

Author

Listed:
  • Sethi, Rajiv

Abstract

This paper considers finitely repeated games played by procedurally rational players, who sample their available alternatives and use realized payoffs as a basis for strategy selection. The corresponding solution concept is that of (payoff) sampling equilibrium, which is a distribution over strategies that is self-replicating under the sampling procedure. Sampling equilibria are rest points of a disequilibrium dynamic process, and stability with respect to this process can be used as an equilibrium selection criterion. The structure of stable sampling equilibria in symmetric, finitely repeated games is characterized, and illustrated with applications to cooperation and coordination over time.

Suggested Citation

  • Sethi, Rajiv, 2021. "Stable sampling in repeated games," Journal of Economic Theory, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:jetheo:v:197:y:2021:i:c:s0022053121001605
    DOI: 10.1016/j.jet.2021.105343
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053121001605
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2021.105343?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. Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
    2. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    3. Bergstrom, Theodore C, 1995. "On the Evolution of Altruistic Ethical Rules for Siblings," American Economic Review, American Economic Association, vol. 85(1), pages 58-81, March.
    4. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    5. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    6. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    7. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    8. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    9. 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).
    10. Jonathan Newton, 2017. "The preferences of Homo Moralis are unstable under evolving assortativity," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 583-589, May.
    11. Ingela Alger & Jörgen W. Weibull, 2013. "Homo Moralis—Preference Evolution Under Incomplete Information and Assortative Matching," Econometrica, Econometric Society, vol. 81(6), pages 2269-2302, November.
    12. 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.
    13. Dilip Abreu & Faruk Gul, 2000. "Bargaining and Reputation," Econometrica, Econometric Society, vol. 68(1), pages 85-118, January.
    14. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
    15. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
    16. Ran Spiegler, 2006. "The Market for Quacks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1113-1131.
    17. ,, 2006. "Competition over agents with boundedly rational expectations," Theoretical Economics, Econometric Society, vol. 1(2), pages 207-231, June.
    18. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2020. "Stability for best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 185(C).
    19. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
    20. Yuval Salant & Josh Cherry, 2020. "Statistical Inference in Games," Econometrica, Econometric Society, vol. 88(4), pages 1725-1752, July.
    21. 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.
    22. Thorsten Chmura & Werner Güth, 2011. "The Minority of Three-Game: An Experimental and Theoretical Analysis," Games, MDPI, vol. 2(3), pages 1-22, September.
    23. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
    24. César Mantilla & Rajiv Sethi & Juan Camilo Cárdenas, 2020. "Efficiency and stability of sampling equilibrium in public goods games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(2), pages 355-370, April.
    25. Robert Rowthorn & Rajiv Sethi, 2008. "Procedural Rationality and Equilibrium Trust," Economic Journal, Royal Economic Society, vol. 118(530), pages 889-905, July.
    26. Binmore, Kenneth G. & Samuelson, Larry, 1992. "Evolutionary stability in repeated games played by finite automata," Journal of Economic Theory, Elsevier, vol. 57(2), pages 278-305, August.
    27. 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.
    28. Jacek Miękisz & Michał Ramsza, 2013. "Sampling Dynamics of a Symmetric Ultimatum Game," Dynamic Games and Applications, Springer, vol. 3(3), pages 374-386, September.
    29. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    30. Osborne, Martin J. & Rubinstein, Ariel, 2003. "Sampling equilibrium, with an application to strategic voting," Games and Economic Behavior, Elsevier, vol. 45(2), pages 434-441, November.
    31. Michał Ramsza, 2005. "Stability of pure strategy sampling equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 515-521, November.
    32. 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.
    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. Sawa, Ryoji & Wu, Jiabin, 2023. "Statistical inference in evolutionary dynamics," Games and Economic Behavior, Elsevier, vol. 137(C), pages 294-316.
    2. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2023. "Strategy sets closed under payoff sampling," Games and Economic Behavior, Elsevier, vol. 138(C), pages 126-142.
    3. Ryoji Sawa, 2022. "Statistical Inference in Evolutionary Dynamics," Working Papers e170, Tokyo Center for Economic Research.
    4. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2022. "Stability of strict equilibria in best experienced payoff dynamics: Simple formulas and applications," Journal of Economic Theory, Elsevier, vol. 206(C).
    5. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2023. "Heterogeneous Noise and Stable Miscoordination," Papers 2305.10301, arXiv.org.

    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. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2022. "Stability of strict equilibria in best experienced payoff dynamics: Simple formulas and applications," Journal of Economic Theory, Elsevier, vol. 206(C).
    2. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2023. "Strategy sets closed under payoff sampling," Games and Economic Behavior, Elsevier, vol. 138(C), pages 126-142.
    3. 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).
    4. 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.
    5. Arigapudi, Srinivas & Heller, Yuval & Schreiber, Amnon, 2021. "Sampling Dynamics and Stable Mixing in Hawk–Dove Games," MPRA Paper 108819, University Library of Munich, Germany.
    6. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    7. Sawa, Ryoji & Wu, Jiabin, 2023. "Statistical inference in evolutionary dynamics," Games and Economic Behavior, Elsevier, vol. 137(C), pages 294-316.
    8. 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.
    9. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2021. "Sampling dynamics and stable mixing in hawk-dove games," Papers 2107.08423, arXiv.org, revised Jun 2022.
    10. Ryoji Sawa, 2022. "Statistical Inference in Evolutionary Dynamics," Working Papers e170, Tokyo Center for Economic Research.
    11. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2023. "Heterogeneous Noise and Stable Miscoordination," Papers 2305.10301, arXiv.org.
    12. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2020. "Stability for best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 185(C).
    13. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    14. 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.
    15. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    16. Abreu, Dilip & Sethi, Rajiv, 2003. "Evolutionary stability in a reputational model of bargaining," Games and Economic Behavior, Elsevier, vol. 44(2), pages 195-216, August.
    17. 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.
    18. Zauner, Klaus G., 1999. "A Payoff Uncertainty Explanation of Results in Experimental Centipede Games," Games and Economic Behavior, Elsevier, vol. 26(1), pages 157-185, January.
    19. Spiegler, Ran, 2005. "Testing threats in repeated games," Journal of Economic Theory, Elsevier, vol. 121(2), pages 214-235, April.
    20. David P. Myatt, 2005. "Instant Exit from the Asymmetric War of Attrition," Economics Series Working Papers 160, University of Oxford, Department of Economics.

    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:jetheo:v:197:y:2021:i:c:s0022053121001605. 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/622869 .

    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.