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The Category of Node-And-Choice Forms for Extensive-Form Games

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Abstract

It would be useful to have a category of extensive-form games whose isomorphisms specify equivalences between games. Toward this goal, Streufert (2016) introduced the category of node-and-choice preforms, where a "preform" is a rooted tree together with choices and information sets. This paper takes another step: It introduces the category of node-and-choice forms, where a "form" is a preform augmented with players. In addition, it derives some consequences of the category's morphisms and provides a characterization of the category's isomorphisms.

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  • Peter A. Streufert, 2016. "The Category of Node-And-Choice Forms for Extensive-Form Games," University of Western Ontario, Departmental Research Report Series 20165, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20165
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    File URL: https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1811&context=economicsresrpt
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    References listed on IDEAS

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    1. Stefano Vannucci, 2007. "Game Formats As Chu Spaces," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 119-138.
    2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    3. 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.
    4. Streufert, Peter A., 2015. "An elementary proof that additive i-likelihood characterizes the supports of consistent assessments," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 37-46.
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    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.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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