Robustness to Strategic Uncertainty

CentER Discussion Paper Series No. 2010-70

32 Pages Posted: 17 Jul 2010 Last revised: 7 Jun 2012

See all articles by Ola Andersson

Ola Andersson

Research Institute of Industrial Economics (IFN); Uppsala University - Department of Economics

Cédric Argenton

Tilburg University - Tilburg University School of Economics and Management; Tilburg Law and Economics Center (TILEC)

Jorgen W. Weibull

Stockholm School of Economics - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Multiple version iconThere are 3 versions of this paper

Date Written: July 10, 2010

Abstract

We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.

Keywords: Nash equilibrium, refinement, strategic uncertainty, price competition, Bertrand competition, bargaining, Nash demand game

JEL Classification: C72, D43, L13

Suggested Citation

Andersson, Ola and Andersson, Ola and Argenton, Cédric and Argenton, Cédric and Weibull, Jorgen W., Robustness to Strategic Uncertainty (July 10, 2010). CentER Discussion Paper Series No. 2010-70, Available at SSRN: https://ssrn.com/abstract=1640466 or http://dx.doi.org/10.2139/ssrn.1640466

Ola Andersson (Contact Author)

Research Institute of Industrial Economics (IFN) ( email )

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HOME PAGE: http://www.ifn.se/medarbetare/forskare/ola-andersson

Uppsala University - Department of Economics ( email )

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Cédric Argenton

Tilburg Law and Economics Center (TILEC) ( email )

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Tilburg University - Tilburg University School of Economics and Management ( email )

P.O. Box 90153
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Jorgen W. Weibull

Stockholm School of Economics - Department of Economics ( email )

P.O. Box 6501
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S-113 83 Stockholm
Sweden

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

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