Refinements of Rationalizability for Normal-Form Games

P.J.J. Herings, V. Vannetelbosch

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Abstract

In normal-form games, rationalizability (Bernheim [3], Pearce [11]) on its own fails to exclude some very implausible strategy choices. Three main refinements of rationalizability have been proposed in the literature: cautious, perfect, and proper rationalizability. Nevertheless, some of these refinements also fail to eliminate unreasonable outcomes and suffer from several drawbacks. Therefore, we introduce the trembling-hand rationalizability concept, where the players' actions have to be best responses also against perturbed conjectures. We also propose another refinement: weakly perfect rationalizability, where players' actions that are not best responses are only played with a very small probability. We show the relationship between perfect rationalizability and weakly perfect rationalizability as well as the relationship between proper rationalizability and weakly perfect rationalizability : weakly perfect rationalizability is a weaker refinement than both perfect and proper rationalizability. Moreover, in two-player games it holds that weakly perfect rationalizability is a weaker refinement than trembling-hand rationalizability. The other relationships between the various refinements are illustrated by means of examples. For the relationship between any other two refinements we give examples showing that the remaining set of strategies corresponding to the first redinement can be either smaller or larger than the one corresponding to the second refinement.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages26
Volume1997-03
Publication statusPublished - 1997

Publication series

NameCentER Discussion Paper
Volume1997-03

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Normal Form
Refinement
Game
Eliminate
Relationships

Keywords

  • rationalizability
  • refinements

Cite this

Herings, P. J. J., & Vannetelbosch, V. (1997). Refinements of Rationalizability for Normal-Form Games. (CentER Discussion Paper; Vol. 1997-03). Tilburg: Microeconomics.
Herings, P.J.J. ; Vannetelbosch, V. / Refinements of Rationalizability for Normal-Form Games. Tilburg : Microeconomics, 1997. (CentER Discussion Paper).
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Herings, PJJ & Vannetelbosch, V 1997 'Refinements of Rationalizability for Normal-Form Games' CentER Discussion Paper, vol. 1997-03, Microeconomics, Tilburg.

Refinements of Rationalizability for Normal-Form Games. / Herings, P.J.J.; Vannetelbosch, V.

Tilburg : Microeconomics, 1997. (CentER Discussion Paper; Vol. 1997-03).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

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N2 - In normal-form games, rationalizability (Bernheim [3], Pearce [11]) on its own fails to exclude some very implausible strategy choices. Three main refinements of rationalizability have been proposed in the literature: cautious, perfect, and proper rationalizability. Nevertheless, some of these refinements also fail to eliminate unreasonable outcomes and suffer from several drawbacks. Therefore, we introduce the trembling-hand rationalizability concept, where the players' actions have to be best responses also against perturbed conjectures. We also propose another refinement: weakly perfect rationalizability, where players' actions that are not best responses are only played with a very small probability. We show the relationship between perfect rationalizability and weakly perfect rationalizability as well as the relationship between proper rationalizability and weakly perfect rationalizability : weakly perfect rationalizability is a weaker refinement than both perfect and proper rationalizability. Moreover, in two-player games it holds that weakly perfect rationalizability is a weaker refinement than trembling-hand rationalizability. The other relationships between the various refinements are illustrated by means of examples. For the relationship between any other two refinements we give examples showing that the remaining set of strategies corresponding to the first redinement can be either smaller or larger than the one corresponding to the second refinement.

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Herings PJJ, Vannetelbosch V. Refinements of Rationalizability for Normal-Form Games. Tilburg: Microeconomics. 1997. (CentER Discussion Paper).