IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v48y2019i2d10.1007_s00182-018-0640-z.html
   My bibliography  Save this article

Catch games: the impact of modeling decisions

Author

Listed:
  • János Flesch

    (Maastricht University)

  • Dries Vermeulen

    (Maastricht University)

  • Anna Zseleva

    (Higher School of Economics)

Abstract

We examine the guarantee levels of the players in a type of zero sum games. We show how these levels depend on the sigma algebras that are being employed on the players’ action spaces. We further argue that guarantee levels may therefore also depend on set theoretic considerations. Additionally, we calculate the guarantee levels for finitely additive strategies. The solutions of catch games essentially differ among these setups. We find optimal strategies for almost all cases.

Suggested Citation

  • János Flesch & Dries Vermeulen & Anna Zseleva, 2019. "Catch games: the impact of modeling decisions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 513-541, June.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:2:d:10.1007_s00182-018-0640-z
    DOI: 10.1007/s00182-018-0640-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-018-0640-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00182-018-0640-z?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. A. Maitra & W. Sudderth, 1998. "Finitely additive stochastic games with Borel measurable payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 257-267.
    2. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    3. Capraro, Valerio & Scarsini, Marco, 2013. "Existence of equilibria in countable games: An algebraic approach," Games and Economic Behavior, Elsevier, vol. 79(C), pages 163-180.
    4. Harris, Christopher J. & Stinchcombe, Maxwell B. & Zame, William R., 2005. "Nearly compact and continuous normal form games: characterizations and equilibrium existence," Games and Economic Behavior, Elsevier, vol. 50(2), pages 208-224, February.
    5. Hans Peters & Dries Vermeulen, 2012. "WPO, COV and IIA bargaining solutions for non-convex bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 851-884, November.
    6. Vincent P. Crawford & Nagore Iriberri, 2007. "Fatal Attraction: Salience, Naïveté, and Sophistication in Experimental "Hide-and-Seek" Games," American Economic Review, American Economic Association, vol. 97(5), pages 1731-1750, December.
    7. Maitra, A & Sudderth, W, 1993. "Finitely Additive and Measurable Stochastic Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 201-223.
    8. Flesch, János & Vermeulen, Dries & Zseleva, Anna, 2017. "Zero-sum games with charges," Games and Economic Behavior, Elsevier, vol. 102(C), pages 666-686.
    9. , R., 2007. "Can intergenerational equity be operationalized?," Theoretical Economics, Econometric Society, vol. 2(2), June.
    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. Flesch, János & Vermeulen, Dries & Zseleva, Anna, 2017. "Zero-sum games with charges," Games and Economic Behavior, Elsevier, vol. 102(C), pages 666-686.
    2. János Flesch & Dries Vermeulen & Anna Zseleva, 2021. "Legitimate equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 787-800, December.
    3. Flesch, Janos & Vermeulen, Dries & Zseleva, Anna, 2018. "Existence of justifiable equilibrium," Research Memorandum 016, Maastricht University, Graduate School of Business and Economics (GSBE).
    4. Capraro, Valerio & Scarsini, Marco, 2013. "Existence of equilibria in countable games: An algebraic approach," Games and Economic Behavior, Elsevier, vol. 79(C), pages 163-180.
    5. Hugo Gimbert & Jérôme Renault & Sylvain Sorin & Xavier Venel & Wieslaw Zielonka, 2016. "On the values of repeated games with signals," PSE-Ecole d'économie de Paris (Postprint) hal-01006951, HAL.
    6. William D. Sudderth, 2016. "Finitely Additive Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 92-108, February.
    7. Bosch-Domènech, Antoni & Vriend, Nicolaas J., 2013. "On the role of non-equilibrium focal points as coordination devices," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 52-67.
    8. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    9. Cairns, Robert D. & Del Campo, Stellio & Martinet, Vincent, 2019. "Sustainability of an economy relying on two reproducible assets," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 145-160.
    10. Asheim, Geir B. & d'Aspremont, Claude & Banerjee, Kuntal, 2010. "Generalized time-invariant overtaking," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 519-533, July.
    11. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    12. Subhasish Chowdhury & Dan Kovenock & Roman Sheremeta, 2013. "An experimental investigation of Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 833-861, April.
    13. Adachi, Tsuyoshi & Cato, Susumu & Kamaga, Kohei, 2014. "Extended anonymity and Paretian relations on infinite utility streams," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 24-32.
    14. Dengler, Sebastian & Prüfer, Jens, 2021. "Consumers' privacy choices in the era of big data," Games and Economic Behavior, Elsevier, vol. 130(C), pages 499-520.
    15. Binswanger, Johannes & Prüfer, Jens, 2012. "Democracy, populism, and (un)bounded rationality," European Journal of Political Economy, Elsevier, vol. 28(3), pages 358-372.
    16. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2021. "Subgame Maxmin Strategies in Zero-Sum Stochastic Games with Tolerance Levels," Dynamic Games and Applications, Springer, vol. 11(4), pages 704-737, December.
    17. Alcocer, Christian Diego & Jeitschko, Thomas D. & Shupp, Robert, 2020. "Naive and sophisticated mixing: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 170(C), pages 157-173.
    18. Manski, Charles F. & Neri, Claudia, 2013. "First- and second-order subjective expectations in strategic decision-making: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 232-254.
    19. Lee, Natalie, 2023. "Feigning ignorance for long-term gains," Games and Economic Behavior, Elsevier, vol. 138(C), pages 42-71.
    20. Shapiro, Dmitry & Shi, Xianwen & Zillante, Artie, 2014. "Level-k reasoning in a generalized beauty contest," Games and Economic Behavior, Elsevier, vol. 86(C), pages 308-329.

    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:spr:jogath:v:48:y:2019:i:2:d:10.1007_s00182-018-0640-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.