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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.

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  • 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, 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
    8. Klaus Ritzberger, 1999. "Recall in extensive form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 69-87.
    9. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    10. Gilboa, Itzhak, 1997. "A Comment on the Absent-Minded Driver Paradox," Games and Economic Behavior, Elsevier, vol. 20(1), pages 25-30, July.
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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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    Keywords

    game tree; extensive form game;

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