IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1802.04595.html
   My bibliography  Save this paper

Knowledge and Unanimous Acceptance of Core Payoffs: An Epistemic Foundation for Cooperative Game Theory

Author

Listed:
  • Shuige Liu

Abstract

We provide an epistemic foundation for cooperative games by proof theory via studying the knowledge for players unanimously accepting only core payoffs. We first transform each cooperative game into a decision problem where a player can accept or reject any payoff vector offered to her based on her knowledge about available cooperation. Then we use a modified KD-system in epistemic logic, which can be regarded as a counterpart of the model for non-cooperative games in Bonanno (2008), (2015), to describe a player's knowledge, decision-making criterion, and reasoning process; especially, a formula called C-acceptability is defined to capture the criterion for accepting a core payoff vector. Within this syntactical framework, we characterize the core of a cooperative game in terms of players' knowledge. Based on that result, we discuss an epistemic inconsistency behind Debreu-Scarf Theorem, that is, the increase of the number of replicas has invariant requirement on each participant's knowledge from the aspect of competitive market, while requires unbounded epistemic ability players from the aspect of cooperative game.

Suggested Citation

  • Shuige Liu, 2018. "Knowledge and Unanimous Acceptance of Core Payoffs: An Epistemic Foundation for Cooperative Game Theory," Papers 1802.04595, arXiv.org, revised Jan 2019.
    • Handle: RePEc:arx:papers:1802.04595
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1802.04595
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Shapley, Lloyd S., 1977. "The St. Petersburg paradox: A con games?," Journal of Economic Theory, Elsevier, vol. 14(2), pages 439-442, April.
    3. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    4. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    5. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396, October.
    6. Shapley, L S, 1975. "An Example of a Slow-Converging Core," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 345-351, June.
    7. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    8. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    9. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, December.
    10. Samuel Bowles & Alan Kirman & Rajiv Sethi, 2017. "Retrospectives: Friedrich Hayek and the Market Algorithm," Journal of Economic Perspectives, American Economic Association, vol. 31(3), pages 215-230, Summer.
    11. Kannai, Yakar, 1992. "The core and balancedness," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 12, pages 355-395, Elsevier.
    12. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915, October.
    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. Tsakas, Elias, 2014. "Epistemic equivalence of extended belief hierarchies," Games and Economic Behavior, Elsevier, vol. 86(C), pages 126-144.
    2. Joseph Y. Halpern & Yoram Moses, 2017. "Characterizing solution concepts in terms of common knowledge of rationality," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 457-473, May.
    3. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    4. Furth, Dave, 1998. "The core of the inductive limit of a direct system of economies with a communication structure," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 433-472, November.
    5. Lorenzo Bastianello & Mehmet S. Ismail, 2022. "Rationality and correctness in n-player games," Papers 2209.09847, arXiv.org, revised Dec 2023.
    6. Tsakas, E., 2012. "Rational belief hierarchies," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    8. Tsakas, E., 2012. "Pairwise mutual knowledge and correlated rationalizability," Research Memorandum 031, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Roger A McCain, 2013. "Value Solutions in Cooperative Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8528, August.
    10. Shuige Liu & Fabio Maccheroni, 2021. "Quantal Response Equilibrium and Rationalizability: Inside the Black Box," Papers 2106.16081, arXiv.org, revised Mar 2024.
    11. Tsakas, Elias, 2013. "Pairwise epistemic conditions for correlated rationalizability," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 379-384.
    12. Tsakas, Elias, 2014. "Rational belief hierarchies," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 121-127.
    13. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    14. Perea, Andrés, 2017. "Forward induction reasoning and correct beliefs," Journal of Economic Theory, Elsevier, vol. 169(C), pages 489-516.
    15. Alexander Kovalenkov & Myrna Wooders, 2003. "Advances in the theory of large cooperative games and applications to club theory; the side payments case," Chapters, in: Carlo Carraro (ed.), The Endogenous Formation of Economic Coalitions, chapter 1, Edward Elgar Publishing.
    16. Giacomo Bonanno, 2018. "Behavior and deliberation in perfect-information games: Nash equilibrium and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 1001-1032, September.
    17. Xiao Luo & Ben Wang, 2022. "An epistemic characterization of MACA," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 995-1024, June.
    18. Andrés Perea & Arkadi Predtetchinski, 2019. "An epistemic approach to stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 181-203, March.
    19. Bach, Christian W. & Perea, Andrés, 2020. "Two definitions of correlated equilibrium," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 12-24.
    20. Andrés Perea & Elias Tsakas, 2019. "Limited focus in dynamic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 571-607, June.

    More about this item

    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:arx:papers:1802.04595. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.