The order independence of iterated dominance in extensive games
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Chen-2013-The order independen.pdf
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Author(s)
Chen, Jing
Micali, Silvio
Date Issued
January 2013
Journal
Theoretical Economics
Publisher
The Econometric Society
Citation
Chen, Jing, and Silvio Micali. “The Order Independence of Iterated Dominance in Extensive Games.” Theoretical Economics 8.1 (2013): 125–163.
Version
Final published version
Abstract
Shimoji and Watson (1998) prove that a strategy of an extensive game is rationalizable
in the sense of Pearce if and only if it survives the maximal elimination of conditionally dominated strategies. Briefly, this process iteratively eliminates
conditionally dominated strategies according to a specific order, which is also the
start of an order of elimination of weakly dominated strategies. Since the final
set of possible payoff profiles, or terminal nodes, surviving iterated elimination of
weakly dominated strategies may be order-dependent, one may suspect that the
same holds for conditional dominance.
We prove that, although the sets of strategy profiles surviving two arbitrary
elimination orders of conditional dominance may be very different from each
other, they are equivalent in the following sense: for each player i and each pair
of elimination orders, there exists a function φi mapping each strategy of i surviving
the first order to a strategy of i surviving the second order, such that, for every
strategy profile s surviving the first order, the profile (φi(si))i induces the same
terminal node as s does.
To prove our results, we put forward a new notion of dominance and an elementary
characterization of extensive-form rationalizability (EFR) that may be
of independent interest. We also establish connections between EFR and other
existing iterated dominance procedures, using our notion of dominance and our
characterization of EFR.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.3982/te942
