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Equivalences Among Five Game Specifications, Including a New Specification Whose Nodes are Sets of Past Choices

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Abstract

The current literature formally links "OR forms" (named after Osborne and Rubinstein 1994) with "KS forms" (named after Kuhn and Selten by Kline and Luckraz 2016). It also formally links "simple forms" with "AR forms" (both from Alos-Ferrer and Ritzberger 2016, with the former less prominent than the latter). This paper makes three contributions. First, it introduces a fifth game form whose nodes are sets of past choices. Second, it formally links these new "choice-set forms" with OR forms. Third, it formally links KS forms with simple forms. The result is a formal five-way equivalence which provides game theorists with a broad spectrum of alternative game specifications.

Suggested Citation

  • Peter A. Streufert, 2018. "Equivalences Among Five Game Specifications, Including a New Specification Whose Nodes are Sets of Past Choices," University of Western Ontario, Departmental Research Report Series 20183, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20183
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    1. Peter A. Streufert, 2018. "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms," University of Western Ontario, Departmental Research Report Series 20186, University of Western Ontario, Department of Economics.
    2. Peter A. Streufert, 2025. "Specifying a game-theoretic extensive form as an abstract 5-ary relation," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(1), pages 1-53, June.

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