Every Choice Function Is Backwards-Induction Rationalizable

Authors

  • Walter Bossert,

    1. Dept. of Economics and CIREQ, University of Montreal, P.O. Box 6128, Station Downtown, Montreal QC H3C 3J7, Canada; walter.bossert@umontreal.ca
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  • Yves Sprumont

    1. Dept. of Economics and CIREQ, University of Montreal, P.O. Box 6128, Station Downtown, Montreal QC H3C 3J7, Canada; yves.sprumont@umontreal.ca
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    • We thank Sean Horan, Indrajit Ray, a co-editor, and three referees for useful discussions and comments. Financial support from the Fonds de Recherche sur la Société et la Culture of Québec and the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged.


Abstract

A choice function is backwards-induction rationalizable if there exists a finite perfect-information extensive-form game such that for each subset of alternatives, the backwards-induction outcome of the restriction of the game to that subset of alternatives coincides with the choice from that subset. We prove that every choice function is backwards-induction rationalizable.

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