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Choice-Set Forms are Dual to Outcome-Set Forms

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Abstract

Alos-Ferrer and Ritzberger (2013) specify each node in a game tree as the set of outcomes that yet remain conceivable. In contrast, Streufert (2015a) specifies each node as the set of choices that have already been made. The symmetry suggests that the two formulations are "dual" in some sense. In this paper I develop this duality. In particular, I define suitable conversion procedures, and show that there is a one-to-one correspondence between choice-set forms and outcome-set forms. The analysis encompasses discrete forms with finite or infinite horizons.

Suggested Citation

  • 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.
    • Handle: RePEc:uwo:uwowop:20153
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    File URL: https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1258&context=economicsresrpt
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    1. 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.
    2. 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.
    3. Carlos Alós-Ferrer & Klaus Ritzberger, 2005. "Trees and decisions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 763-798, June.
    4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
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    1. 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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