Scandinavian Working Papers in Economics

Working Paper Series,
Research Institute of Industrial Economics

No 910: Robustness to Strategic Uncertainty

Ola Andersson (), Cédric Argenton () and Jörgen W. Weibull ()
Additional contact information
Ola Andersson: Research Institute of Industrial Economics (IFN), Postal: P.O. Box 55665, SE-102 15 Stockholm, Sweden
Cédric Argenton: CentER & TILEC, Postal: Tilburg University
Jörgen W. Weibull: Stockholm School of Economics, Postal: Ecole Polytechnique (Paris) and Royal Institute of Technology (Stockholm)

Abstract: In games with continuum strategy sets, we model a player’s uncertainty about another player’s strategy, as an atomless probability distribution over the other player’s strategy set. 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 which every player’s strategy is optimal under his or her uncertainty about the others. General properties of this robustness criterion are derived and it is shown that it is a refinement of Nash equilibrium when payoff functions are continuous. We apply the criterion to a class of Bertrand competition games. These are discontinuous games that admit a continuum of Nash equilibria. Our robustness criterion selects a unique Nash equilibrium, and this selection agrees with recent experimental findings.

Keywords: Nash equilibrium; Refinement; Strategic uncertainty; Bertrand competition; Log-concavity

JEL-codes: C72; D43; L13

27 pages, March 30, 2012

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