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Specifying Nodes as Sets of Choices

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Abstract

Osborne and Rubinstein (1994) specify each node in a game tree as a sequence of actions. It is well-known that such actions can be replaced by choices (i.e. agent-specific actions) without loss of generality. I find that this sequential formulation is redundant in the sense that nodes can be equivalently specified as sets of choices. The only cost of doing so is to rule out absent-mindedness. My analysis encompasses both ordered and unordered information sets and both finite and infinite horizons. (This specification of nodes as sets of choices differs from the literature's specification of nodes as sets of outcomes.)

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  • 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.
    • Handle: RePEc:uwo:uwowop:20151
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    1. 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.
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    Cited by:

    1. Peter A. Streufert, 2016. "The Category of Node-and-Choice Preforms for Extensive-Form Games," University of Western Ontario, Departmental Research Report Series 20162, University of Western Ontario, Department of Economics.
    2. 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.
    3. 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.

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