IDEAS home Printed from https://ideas.repec.org/a/wut/journl/v1y2014p71-96id1074.html
   My bibliography  Save this article

Probabilities on streams and reflexive games

Author

Listed:
  • Andrew Schumann

Abstract

Probability measures on streams (e.g. on hypernumbers and p-adic numbers) have been defined. It was shown that these probabilities can be used for simulations of reflexive games. In particular, it can be proved that Aumann’s agreement theorem does not hold for these probabilities. Instead of this theorem, there is a statement that is called the reflexion disagreement theorem. Based on this theorem, probabilistic and knowledge conditions can be defined for reflexive games at various reflexion levels up to the infinite level.

Suggested Citation

  • Andrew Schumann, 2014. "Probabilities on streams and reflexive games," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(1), pages 71-96.
    • Handle: RePEc:wut:journl:v:1:y:2014:p:71-96:id:1074
    DOI: 10.5277/ord140105
    as

    Download full text from publisher

    File URL: https://ord.pwr.edu.pl/assets/papers_archive/1074%20-%20published.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.5277/ord140105?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
    ---><---

    References listed on IDEAS

    as
    1. Pierre Lescanne & Matthieu Perrinel, 2012. "''Backward'' Coinduction, Nash equilibrium and the Rationality of Escalation," Post-Print ensl-00692767, HAL.
    2. Heifetz, Aviad, 1996. "Non-well-founded-Type Spaces," Games and Economic Behavior, Elsevier, vol. 16(2), pages 202-217, October.
    3. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    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. Daron Acemoglu & Matthew O. Jackson, 2017. "Social Norms and the Enforcement of Laws," Journal of the European Economic Association, European Economic Association, vol. 15(2), pages 245-295.
    2. Ernesto Dal Bó & Pedro Dal Bó & Rafael Di Tella, 2007. "Reputation When Threats and Transfers Are Available," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 16(3), pages 577-598, September.
    3. Carmona, Guilherme & Carvalho, Luís, 2016. "Repeated two-person zero-sum games with unequal discounting and private monitoring," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 131-138.
    4. , H. & ,, 2016. "Approximate efficiency in repeated games with side-payments and correlated signals," Theoretical Economics, Econometric Society, vol. 11(1), January.
    5. Matsushima Hitoshi, 2020. "Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 20(1), pages 1-11, January.
    6. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2012. "Communication and Learning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(2), pages 419-450.
    7. Do, Jihwan & Miklós-Thal, Jeanine, 2023. "Partial secrecy in vertical contracting," International Journal of Industrial Organization, Elsevier, vol. 90(C).
    8. Contou-Carrère, Pauline & Tomala, Tristan, 2011. "Finitely repeated games with semi-standard monitoring," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 14-21, January.
    9. Jayakumar Subramanian & Amit Sinha & Aditya Mahajan, 2023. "Robustness and Sample Complexity of Model-Based MARL for General-Sum Markov Games," Dynamic Games and Applications, Springer, vol. 13(1), pages 56-88, March.
    10. Hart, Sergiu & Rinott, Yosef, 2020. "Posterior probabilities: Dominance and optimism," Economics Letters, Elsevier, vol. 194(C).
    11. W. Bentley MacLeod, 2006. "Reputations, Relationships and the Enforcement of Incomplete Contracts," CESifo Working Paper Series 1730, CESifo.
    12. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    13. Daron Acemoglu & Matthew O. Jackson, 2015. "History, Expectations, and Leadership in the Evolution of Social Norms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(2), pages 423-456.
    14. Chatterjee, Satyajit & Corbae, Dean & Ríos-Rull, José-Víctor, 2008. "A finite-life private-information theory of unsecured consumer debt," Journal of Economic Theory, Elsevier, vol. 142(1), pages 149-177, September.
    15. Attanasi, Giuseppe & Battigalli, Pierpaolo & Manzoni, Elena & Nagel, Rosemarie, 2019. "Belief-dependent preferences and reputation: Experimental analysis of a repeated trust game," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 341-360.
    16. Sofia Moroni, 2018. "Games with Private Timing," Working Paper 6400, Department of Economics, University of Pittsburgh.
    17. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 99-125, January.
    18. Fausti, Scott W. & Qasmi, Bashir A. & Diersen, Matthew A & Adamson, Bill, 2014. "Grid Valuation of Beef Carcass Quality: Market Power and Market Trends," Economics Staff Papers 171423, South Dakota State University, Department of Economics.
    19. John Tyson Chatagnier, 2015. "Conflict bargaining as a signal to third parties," Journal of Theoretical Politics, , vol. 27(2), pages 237-268, April.
    20. Matros, Alexander & Smirnov, Vladimir, 2016. "Duplicative search," Games and Economic Behavior, Elsevier, vol. 99(C), pages 1-22.

    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:wut:journl:v:1:y:2014:p:71-96:id:1074. 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: Adam Kasperski (email available below). General contact details of provider: https://edirc.repec.org/data/iopwrpl.html .

    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.