Robustness to Strategic Uncertainty
CentER Discussion Paper Series No. 2010-70
32 Pages Posted: 17 Jul 2010 Last revised: 7 Jun 2012
Date Written: July 10, 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. 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: Suggested Citation