Robustness to Strategic Uncertainty
Tilburg University CentER Discussion Paper No. 2010-98 (Revision of 2010-70)
32 Pages Posted: 30 Sep 2010 Last revised: 22 Jul 2011
Date Written: July 1, 2010
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.
Keywords: Nash Equilibrium, Refinement, Strategic Uncertainty, Price Competition
JEL Classification: C72, D43, L13
Suggested Citation: Suggested Citation