PP-2004-25: Minimal belief revision leads to backward induction

PP-2004-25: Perea, Andrés (2004) Minimal belief revision leads to backward induction. [Report]

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In this paper we present a model for games with perfect information in
which the players, upon observing an unexpected move, may revise their
beliefs about the opponents' preferences over outcomes. For a given
profile P of preference relations over outcomes, we impose the
following three principles: (1) players initially believe that
opponents have preference relations as specified by P ; (2) players
believe at every instance of the game that each opponent is carrying
out an optimal strategy; and (3) beliefs about the opponents'
preference relations over outcomes should be revised in a minimal
way. It is shown that every player whose preference relation is given
by P, and who throughout the game respects common belief in the events
(1), (2) and (3), has a unique optimal strategy, namely his backward
induction strategy in the game induced by P. We finally show that
replacing the minimal belief revision principle (3) by the more modest
requirement of Bayesian updating leads exactly to the Dekel-Fudenberg
procedure in the game induced by P.

Item Type: Report
Report Nr: PP-2004-25
Series Name: Prepublication (PP) Series
Year: 2004
Uncontrolled Keywords: backward induction; belief revision; preferences; games
Depositing User: Benedikt
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/136

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