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The Category of Node-and-Choice Preforms 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. Since working with entire games is too large a project for a single paper, I begin here with preforms, where a “preform” is a rooted tree together with choices and information sets. My first contribution is to introduce a compact preform specification called a “node-and-choice” preform. This specification’s compactness allows me to introduce tractable morphisms which map one node-and-choice preform to another. I incorporate these morphisms into a category called the “category of node-and-choice preforms”. Finally, I characterize the isomorphisms of this category.

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  • 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.
    • Handle: RePEc:uwo:uwowop:20162
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    1. Peter A. Streufert, 2015. "Specifying Nodes as Sets of Choices," University of Western Ontario, Departmental Research Report Series 20151, University of Western Ontario, Department of Economics.
    2. 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.
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    Cited by:

    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. Peter A. Streufert, 2020. "The Category of Node-and-Choice Extensive-Form Games," Papers 2004.11196, arXiv.org, revised Jul 2020.

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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.
    2. 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.
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    4. Peter A. Streufert, 2015. "Choice-Set Forms are Dual to Outcome-Set Forms," University of Western Ontario, Departmental Research Report Series 20153, University of Western Ontario, Department of Economics.

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