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Equivalences among five game specifications, including a new specification whose nodes are sets of past choices

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  • Peter A. Streufert

    (Western University)

Abstract

The current literature formally links “OR forms” (named after Osborne and Rubinstein, in A course in game theory. MIT, London, 1994) with “KS forms” (named after Kuhn and Selten by Kline and Luckraz, in Econ Theory Bull 4:85–94, 2016). It also formally links “simple forms” with “AR forms” (the former is less prominent than the latter, and both are from Alós-Ferrer and Ritzberger, in The theory of extensive form games. Springer, Berlin, 2016a). 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, 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.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:1:d:10.1007_s00182-018-0652-8
    DOI: 10.1007/s00182-018-0652-8
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    References listed on IDEAS

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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. 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.

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    Keywords

    Game tree; Extensive form game;

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