IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v256y2015icp267-275.html

Group-separations based on the repeated prisoners’ dilemma games

Author

Listed:
  • Huang, Yuankan
  • Inohara, Takehiro

Abstract

We model group-separations in an n-player set. In the n-player set, every two players play an infinitely repeated two-player prisoners’ dilemma game. Each player takes a mixed strategy to play the game and trigger strategy is used to punish the deviator. Let all players share a common discount factor δ. We find that with the variation of δ, the n-player set is separated into several subsets such that (1) for any two players in any two different subsets, their strategy profile is not a subgame perfect equilibrium and (2) each subset cannot be separated into several subsets that satisfy (1). Such subsets are called groups and the separation is called group-separation. We aim to specify the intervals (of δ) such that group-separations emerge. Particularly, we focus on the relationship between the interval and the form of each group-separation.

Suggested Citation

  • Huang, Yuankan & Inohara, Takehiro, 2015. "Group-separations based on the repeated prisoners’ dilemma games," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 267-275.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:267-275
    DOI: 10.1016/j.amc.2015.01.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315000545
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.01.040?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Maruta, Toshimasa & Okada, Akira, 2012. "Dynamic group formation in the repeated prisonerʼs dilemma," Games and Economic Behavior, Elsevier, vol. 74(1), pages 269-284.
    2. Xia, Chengyi & Miao, Qin & Zhang, Juanjuan, 2013. "Impact of neighborhood separation on the spatial reciprocity in the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 22-30.
    3. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    4. van Damme, Eric, 1989. "Renegotiation-proof equilibria in repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 47(1), pages 206-217, February.
    5. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    7. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    8. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
      • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
    9. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    10. Zhi-Qin Ma & Cheng-Yi Xia & Shi-Wen Sun & Li Wang & Huai-Bin Wang & Juan Wang, 2011. "Heterogeneous Link Weight Promotes The Cooperation In Spatial Prisoner'S Dilemma," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(11), pages 1257-1268.
    Full references (including those not matched with items on IDEAS)

    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. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    2. Aramendia, Miguel & Wen, Quan, 2014. "Justifiable punishments in repeated games," Games and Economic Behavior, Elsevier, vol. 88(C), pages 16-28.
    3. Calvo-Armengol, Antoni, 2001. "Bargaining power in communication networks," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 69-87, January.
    4. Dutta, Bhaskar & Ghosal, Sayantan & Ray, Debraj, 2005. "Farsighted network formation," Journal of Economic Theory, Elsevier, vol. 122(2), pages 143-164, June.
    5. Anna PAPACCIO, 2013. "Bilateralism and Multilateralism: a Network Approach," CELPE Discussion Papers 125, CELPE - CEnter for Labor and Political Economics, University of Salerno, Italy.
    6. Slikker, M. & van den Nouweland, C.G.A.M., 1999. "Network Formation Models With Costs for Establishing Links," Research Memorandum 771, Tilburg University, School of Economics and Management.
    7. Vartiainen, Hannu, 2011. "Dynamic coalitional equilibrium," Journal of Economic Theory, Elsevier, vol. 146(2), pages 672-698, March.
    8. Slikker, Marco & van den Nouweland, Anne, 2001. "A One-Stage Model of Link Formation and Payoff Division," Games and Economic Behavior, Elsevier, vol. 34(1), pages 153-175, January.
    9. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, University Library of Munich, Germany.
    10. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    11. Joost Vandenbossche & Thomas Demuynck, 2013. "Network Formation with Heterogeneous Agents and Absolute Friction," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 23-45, June.
    12. Michael Kosfeld, "undated". "Network Experiments," IEW - Working Papers 152, Institute for Empirical Research in Economics - University of Zurich.
    13. Matthew O. Jackson, 2003. "A survey of models of network formation: Stability and efficiency," Working Papers 1161, California Institute of Technology, Division of the Humanities and Social Sciences.
    14. Kleinberg, Jon & Ligett, Katrina, 2013. "Information-sharing in social networks," Games and Economic Behavior, Elsevier, vol. 82(C), pages 702-716.
    15. Larry Samuelson, 2016. "Game Theory in Economics and Beyond," Journal of Economic Perspectives, American Economic Association, vol. 30(4), pages 107-130, Fall.
    16. Marco Marini, 2007. "An Overview of Coalition & Network Formation Models for Economic Applications," Working Papers 0712, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2007.
    17. Francis Bloch & Matt Jackson, 2004. "The Formation of Networks with Side Payments," Econometric Society 2004 North American Summer Meetings 198, Econometric Society.
    18. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    19. Syngjoo Choi & Edoardo Gallo & Shachar Kariv, 2015. "Networks in the laboratory," Cambridge Working Papers in Economics 1551, Faculty of Economics, University of Cambridge.
    20. Roland Pongou & Roberto Serrano, 2009. "A Dynamic Theory of Fidelity Networks with an Application to the Spread of HIV / AIDS," Working Papers wp2009_0909, CEMFI.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:eee:apmaco:v:256:y:2015:i:c:p:267-275. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.