IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2004.11196.html
   My bibliography  Save this paper

The Category of Node-and-Choice Extensive-Form Games

Author

Listed:
  • Peter A. Streufert

Abstract

This paper develops the category $\mathbf{NCG}$. Its objects are node-and-choice games, which include essentially all extensive-form games. Its morphisms allow arbitrary transformations of a game's nodes, choices, and players, as well as monotonic transformations of the utility functions of the game's players. Among the morphisms are subgame inclusions. Several characterizations and numerous properties of the isomorphisms are derived. For example, it is shown that isomorphisms preserve the game-theoretic concepts of no-absentmindedness, perfect-information, and (pure-strategy) Nash-equilibrium. Finally, full subcategories are defined for choice-sequence games and choice-set games, and relationships among these two subcategories and $\mathbf{NCG}$ itself are expressed and derived via isomorphic inclusions and equivalences.

Suggested Citation

  • Peter A. Streufert, 2020. "The Category of Node-and-Choice Extensive-Form Games," Papers 2004.11196, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:2004.11196
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2004.11196
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Machover, Moshé & Terrington, Simon D., 2014. "Mathematical structures of simple voting games," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 61-68.
    2. Piccione, Michele & Rubinstein, Ariel, 1997. "On the Interpretation of Decision Problems with Imperfect Recall," Games and Economic Behavior, Elsevier, vol. 20(1), pages 3-24, July.
    3. Bonanno, G, 1992. "Set-Theoretic Equivalence of Extensive-Form Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 429-447.
    4. Elmes Susan & Reny Philip J., 1994. "On the Strategic Equivalence of Extensive Form Games," Journal of Economic Theory, Elsevier, vol. 62(1), pages 1-23, February.
    5. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    6. Carlos Alós-Ferrer & Klaus Ritzberger, 2016. "The Theory of Extensive Form Games," Springer Series in Game Theory, Springer, number 978-3-662-49944-3, March.
    7. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    8. Victor Lapitsky, 1999. "On Some Categories Of Games And Corresponding Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 169-185.
    9. Peter A. Streufert, 2016. "The Category of Node-and-Choice Preforms for Extensive-Form Games," University of Western Ontario, Departmental Research Report Series 20162, University of Western Ontario, Department of Economics.
    10. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    11. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-628, May.
    12. J. Jude Kline & Shravan Luckraz, 2016. "Equivalence between graph-based and sequence-based extensive form games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 85-94, April.
    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. Streufert, Peter, 2018. "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms," MPRA Paper 90490, University Library of Munich, Germany.
    2. Battigalli, Pierpaolo & Leonetti, Paolo & Maccheroni, Fabio, 2020. "Behavioral equivalence of extensive game structures," Games and Economic Behavior, Elsevier, vol. 121(C), pages 533-547.
    3. Peter A. Streufert, 2021. "A Category for Extensive-Form Games," Papers 2105.11398, arXiv.org.
    4. Soo Hong Chew & Wenqian Wang, 2022. "Information Design of Dynamic Mechanisms," Papers 2205.10844, arXiv.org.
    5. Peter A. Streufert, 2019. "Equivalences among five game specifications, including a new specification whose nodes are sets of past choices," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 1-32, March.
    6. Pierpaolo Battigalli & Nicolò Generoso, 2021. "Information Flows and Memory in Games," Working Papers 678, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Carlos Alós-Ferrer & Klaus Ritzberger, 2020. "Reduced normal forms are not extensive forms," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 281-288, October.
    8. Carlos Alós-Ferrer & Klaus Ritzberger, 2013. "Large extensive form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 75-102, January.
    9. Hillas, John & Kvasov, Dmitriy, 2020. "Backward induction in games without perfect recall," Games and Economic Behavior, Elsevier, vol. 124(C), pages 207-218.
    10. Pierpaolo Battigalli & Martin Dufwenberg, 2022. "Belief-Dependent Motivations and Psychological Game Theory," Journal of Economic Literature, American Economic Association, vol. 60(3), pages 833-882, September.
    11. Shravan Luckraz & Bruno Antonio Pansera, 2022. "A Note on the Concept of Time in Extensive Games," Mathematics, MDPI, vol. 10(8), pages 1-4, April.
    12. Voorneveld, Mark & Fagraeus Lundström, Helena, 2005. "Strategic equivalence and bounded rationality in extensive form games," SSE/EFI Working Paper Series in Economics and Finance 605, Stockholm School of Economics.
    13. Mackenzie, Andrew, 2020. "A revelation principle for obviously strategy-proof implementation," Games and Economic Behavior, Elsevier, vol. 124(C), pages 512-533.
    14. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
    15. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 11, University of California, Davis, Department of Economics.
    16. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    17. Casajus, Andre, 2003. "Weak isomorphism of extensive games," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 267-290, December.
    18. Thijssen, J.J.J., 2003. "Investment under uncertainty, market evolution and coalition spillovers in a game theoretic perspective," Other publications TiSEM 672073a6-492e-4621-8d4a-0, Tilburg University, School of Economics and Management.
    19. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2017. "Does backwards induction imply subgame perfection?," Games and Economic Behavior, Elsevier, vol. 103(C), pages 19-29.
    20. Levent Koçkesen & Efe A. Ok, 2004. "Strategic Delegation By Unobservable Incentive Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(2), pages 397-424.

    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:2004.11196. 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.