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Specifying Nodes as Sets of Actions

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Abstract

The nodes of an extensive-form game are commonly specified as sequences of actions. Rubinstein calls such nodes histories. We find that this sequential notation is superfl uous in the sense that nodes can also be specified as sets of actions. The only cost of doing so is to rule out games with absent-minded agents. Our set-theoretic analysis accommodates general finite-horizon games with arbitrarily large action spaces and arbitrarily configured information sets. One application is Streufert (2012),which specifies nodes as sets in order to formulate and prove new results about Kreps-Wilson consistency.

Suggested Citation

  • Peter A. Streufert, 2012. "Specifying Nodes as Sets of Actions," University of Western Ontario, Departmental Research Report Series 20122, University of Western Ontario, Department of Economics.
    • Handle: RePEc:uwo:uwowop:20122
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    File URL: https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1252&context=economicsresrpt
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    Cited by:

    1. Streufert, Peter A., 2015. "An elementary proof that additive i-likelihood characterizes the supports of consistent assessments," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 37-46.

    More about this item

    Keywords

    game tree; set tree; extensive-form game.;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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