Strong robustness to incomplete information and the uniqueness of a correlated equilibrium

• Published in: Economic theory Vol. 73; no. 1; pp. 91 - 119
• Main Authors: Einy, Ezra, Haimanko, Ori, Lagziel, David
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022; Springer; Springer Nature B.V
• Subjects: Auctions; Bayesian analysis; Economic theory; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Equilibrium; Game Theory; Games; Information; Mediation; Microeconomics; Public Finance; Research Article; Robustness; Social and Behav. Sciences; Uniqueness; Voting; Iran; Nash equilibrium; Strong robustness to incomplete information; Correlated equilibrium; C62; C72; D82
• ISSN: 0938-2259; 1432-0479
• DOI: 10.1007/s00199-020-01327-4

We define and characterize the notion of strong robustness to incomplete information, whereby a Nash equilibrium in a game u is strongly robust if, given that each player knows that his payoffs are those in u with high probability, all Bayesian–Nash equilibria in the corresponding incomplete-information game are close—in terms of action distribution—to that equilibrium of u . We prove, under some continuity requirements on payoffs, that a Nash equilibrium is strongly robust if and only if it is the unique correlated equilibrium. We then review and extend the conditions that guarantee the existence of a unique correlated equilibrium in games with a continuum of actions. The existence of a strongly robust Nash equilibrium is thereby established for several domains of games, including those that arise in economic environments as diverse as Tullock contests, all-pay auctions, Cournot and Bertrand competitions, network games, patent races, voting problems and location games.