TY - JOUR
T1 - Strong robustness to incomplete information and the uniqueness of a correlated equilibrium
AU - Einy, Ezra
AU - Haimanko, Ori
AU - Lagziel, David
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/2/1
Y1 - 2022/2/1
N2 - 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.
AB - 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.
KW - Correlated equilibrium
KW - Nash equilibrium
KW - Strong robustness to incomplete information
UR - http://www.scopus.com/inward/record.url?scp=85096003024&partnerID=8YFLogxK
U2 - 10.1007/s00199-020-01327-4
DO - 10.1007/s00199-020-01327-4
M3 - Article
AN - SCOPUS:85096003024
SN - 0938-2259
VL - 73
SP - 91
EP - 119
JO - Economic Theory
JF - Economic Theory
IS - 1
ER -