IDEAS home Printed from https://ideas.repec.org/p/vnm/wpdman/162.html
   My bibliography  Save this paper

Categorization and cooperation across games

Author

Listed:
  • Marco LiCalzi

    (Dept. of Management, Università Ca' Foscari Venice)

  • Roland Muhlenbernd

    (Dept. of Management, Università Ca' Foscari Venice)

Abstract

We study a model where agents face a continuum of two-player games and categorize them into a finite number of situations to make sense of their complex environment. Each agent can cooperate or defect, conditional on the perceived category. Agents may not share the same categorization. The games are fully ordered by one parameter, interpreted as the temptation to break joint cooperation by defecting. We prove that in equilibrium agents must share the same categorization. Most equilibria achieve less cooperation than it would be possible if agents could fully discriminate games. All the equilibria are evolutionarily stable, but the only stochastically stable profile leads to defection everywhere, destroying all opportunities for cooperation. We then study agents’ social learning when they imitate successful players over similar games, but lack any information about the categorizations of other players. We show how imitation leads to a shared categorization that achieves higher cooperation than under full discrimination.

Suggested Citation

  • Marco LiCalzi & Roland Muhlenbernd, 2018. "Categorization and cooperation across games," Working Papers 14, Department of Management, Università Ca' Foscari Venezia.
  • Handle: RePEc:vnm:wpdman:162
    as

    Download full text from publisher

    File URL: http://virgo.unive.it/wpideas/storage/2018wp14.pdf
    File Function: First version, 2018
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 17-45.
    2. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    3. Arthur T. Denzau & Douglass C. North, 1994. "Shared Mental Models: Ideologies and Institutions," Kyklos, Wiley Blackwell, vol. 47(1), pages 3-31, February.
    4. , & ,, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
    5. Michael Bacharach, 2006. "The Hi-Lo Paradox, from Beyond Individual Choice: Teams and Frames in Game Theory," Introductory Chapters, in: Natalie Gold & Robert Sugden (ed.),Beyond Individual Choice: Teams and Frames in Game Theory, Princeton University Press.
    6. Carlos Gracia-Lázaro & Luis Mario Floría & Yamir Moreno, 2017. "Cognitive Hierarchy Theory and Two-Person Games," Games, MDPI, vol. 8(1), pages 1-18, January.
    7. Hoff, Karla & Stiglitz, Joseph E., 2016. "Striving for balance in economics: Towards a theory of the social determination of behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 126(PB), pages 25-57.
    8. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 997-1026, August.
    9. Bednar, Jenna & Chen, Yan & Liu, Tracy Xiao & Page, Scott, 2012. "Behavioral spillovers and cognitive load in multiple games: An experimental study," Games and Economic Behavior, Elsevier, vol. 74(1), pages 12-31.
    10. Alexander Peysakhovich & David G. Rand, 2016. "Habits of Virtue: Creating Norms of Cooperation and Defection in the Laboratory," Management Science, INFORMS, vol. 62(3), pages 631-647, March.
    11. LiCalzi Marco, 1995. "Fictitious Play by Cases," Games and Economic Behavior, Elsevier, vol. 11(1), pages 64-89, October.
    12. Glenn Ellison & Richard Holden, 2014. "A Theory of Rule Development," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 30(4), pages 649-682.
    13. John Van Huyck & Dale O. Stahl, 2018. "Conditional behavior and learning in similar stag hunt games," Experimental Economics, Springer;Economic Science Association, vol. 21(3), pages 513-526, September.
    14. 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.
    15. Knez, Marc & Camerer, Colin, 2000. "Increasing Cooperation in Prisoner's Dilemmas by Establishing a Precedent of Efficiency in Coordination Games," Organizational Behavior and Human Decision Processes, Elsevier, vol. 82(2), pages 194-216, July.
    16. 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.
    17. Robert Gibbons & Marco LiCalzi & Massimo Warglien, 2017. "What situation is this? Coarse cognition and behavior over a space of games," Working Papers 09, Department of Management, Università Ca' Foscari Venezia.
    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. Daskalova, Vessela & Vriend, Nicolaas J., 2021. "Learning frames," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 78-96.
    2. Marco LiCalzi & Roland Mühlenbernd, 2022. "Feature-weighted categorized play across symmetric games," Experimental Economics, Springer;Economic Science Association, vol. 25(3), pages 1052-1078, June.
    3. Roland Mühlenbernd & Sławomir Wacewicz & Przemysław Żywiczyński, 2022. "The Evolution of Ambiguity in Sender—Receiver Signaling Games," Games, MDPI, vol. 13(2), pages 1-19, February.
    4. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).

    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. Marco LiCalzi & Roland Mühlenbernd, 2022. "Feature-weighted categorized play across symmetric games," Experimental Economics, Springer;Economic Science Association, vol. 25(3), pages 1052-1078, June.
    2. Khan, Abhimanyu, 2021. "Evolutionary Stability of Behavioural Rules," MPRA Paper 112920, University Library of Munich, Germany, revised 01 May 2022.
    3. Friederike Mengel & Emanuela Sciubba, 2010. "Extrapolation in Games of Coordination and Dominance Solvable Games," Working Papers 2010.148, Fondazione Eni Enrico Mattei.
    4. Rossella Argenziano & Itzhak Gilboa, 2012. "History as a coordination device," Theory and Decision, Springer, vol. 73(4), pages 501-512, October.
    5. Dal Bó, Pedro & Fréchette, Guillaume R. & Kim, Jeongbin, 2021. "The determinants of efficient behavior in coordination games," Games and Economic Behavior, Elsevier, vol. 130(C), pages 352-368.
    6. 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.
    7. Cason, Timothy N. & Savikhin, Anya C. & Sheremeta, Roman M., 2012. "Behavioral spillovers in coordination games," European Economic Review, Elsevier, vol. 56(2), pages 233-245.
    8. David J. Cooper & John Van Huyck, 2018. "Coordination and transfer," Experimental Economics, Springer;Economic Science Association, vol. 21(3), pages 487-512, September.
    9. Daskalova, Vessela & Vriend, Nicolaas J., 2020. "Categorization and coordination," European Economic Review, Elsevier, vol. 129(C).
    10. John Duffy & Dietmar Fehr, 2018. "Equilibrium selection in similar repeated games: experimental evidence on the role of precedents," Experimental Economics, Springer;Economic Science Association, vol. 21(3), pages 573-600, September.
    11. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 997-1026, August.
    12. Grimm, Veronika & Mengel, Friederike, 2012. "An experiment on learning in a multiple games environment," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2220-2259.
    13. Daskalova, Vessela & Vriend, Nicolaas J., 2021. "Learning frames," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 78-96.
    14. Sibilla Di Guida & Giovanna Devetag, 2013. "Feature-Based Choice and Similarity Perception in Normal-Form Games: An Experimental Study," Games, MDPI, vol. 4(4), pages 1-19, December.
    15. Mengel, Friederike & Sciubba, Emanuela, 2014. "Extrapolation and structural similarity in games," Economics Letters, Elsevier, vol. 125(3), pages 381-385.
    16. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    17. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    18. Norman, Thomas W.L., 2009. "Rapid evolution under inertia," Games and Economic Behavior, Elsevier, vol. 66(2), pages 865-879, July.
    19. Marchiori, Davide & Di Guida, Sibilla & Polonio, Luca, 2021. "Plasticity of strategic sophistication in interactive decision-making," Journal of Economic Theory, Elsevier, vol. 196(C).
    20. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.

    More about this item

    Keywords

    categorization; cooperation; evolutionary stability; learning by imitation; prisoners' dilemma; stag hunt;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:vnm:wpdman:162. 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://edirc.repec.org/data/mdvenit.html .

    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: Marco LiCalzi (email available below). General contact details of provider: https://edirc.repec.org/data/mdvenit.html .

    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.