Robustness to Strategic Uncertainty - Ola Andersson; Cédric Argenton; Jörgen W. Weibull (Research Institute of Industrial Economics (IFN), 2012)
In games with continuum strategy sets, we model a players uncertainty about another players strategy, as an atomless probability distribution over the other players 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 players 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: C72; D43; L13; 330; Nash equilibrium; Refinement; Strategic uncertainty; Bertrand competition; Log-concavity; Entscheidung bei Unsicherheit; Preiswettbewerb; Nash-Gleichgewicht; Nichtkooperatives Spiel; Theorie