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

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  • 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.

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  • 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
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