In a self-confirming equilibrium, each player correctly forecasts the actio
ns that opponents will take along the equilibrium path, but may be mistaken
about the way that opponents would respond to deviations. This paper devel
ops a refinement of self-confirming equilibrium in which players use inform
ation about opponents' payoffs in forming beliefs about the way that oppone
nts play off of the equilibrium path. We show that this concept is robust t
o payoff uncertainty. We also discuss its relationship to other concepts an
d show that it is closely related to assuming almost common certainty of pa
yoffs in an epistemic model with independent beliefs. Journal of Economic L
iterature Classification Numbers: C72, D84. (C) 1999 Academic Press.