Epistemic Foundation of the Backward Induction Paradox

19 Pages Posted: 28 Nov 2022

See all articles by Geir B. Asheim

Geir B. Asheim

University of Oslo - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Thomas Brunnschweiler

affiliation not provided to SSRN

Abstract

After having observed a deviation from backward induction, a player might deem the opponent prone to deviate from backward induction again, making it worthwhile to deviate himself. Such reaction might make the deviation by the opponent worthwhile in the first place---which is the backward induction paradox. This argument against backward induction cannot be made in games where all players move only once. While strategic-form perfect equilibrium yields backward induction in games where players move only once but not necessarily otherwise, no existing non-equilibrium concept captures the backward induction paradox by having these properties. To provide such a concept, we define and epistemically characterize the Independent Dekel-Fudenberg Procedure. Since beliefs are modelled by non-Archimedean probabilities, meaning that some opponent choices might be assigned subjective probability zero without being deemed subjectively impossible, special attention is paid to the formalization of stochastically independent beliefs.

Keywords: Perfect information games, backward induction paradox, non-Archimedean probabilities, stochastic independence.

Suggested Citation

Asheim, Geir B. and Brunnschweiler, Thomas, Epistemic Foundation of the Backward Induction Paradox. Available at SSRN: https://ssrn.com/abstract=4287512 or http://dx.doi.org/10.2139/ssrn.4287512

Geir B. Asheim (Contact Author)

University of Oslo - Department of Economics ( email )

P.O. Box 1095 Blindern
N-0317 Oslo
Norway
+47-2285 5498 (Phone)
+47-2285 5035 (Fax)

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

HOME PAGE: http://www.CESifo.de

Thomas Brunnschweiler

affiliation not provided to SSRN ( email )

No Address Available

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
30
Abstract Views
250
PlumX Metrics