Most of the results of modern game theory presuppose that the choices
rational agents make in noncooperative games are probabilistically ind
ependent. In this paper I argue that there is no a priori reason for r
ational agents to assume probabilistic independence. I introduce a sol
ution concept for noncooperative games called an endogenous correlated
equilibrium, which generalizes the Nash equilibrium concept by droppi
ng probabilistic independence. I contrast the endogenous correlated eq
uilibrium with the correlated equilibrium defined by Aumann (1974, 198
7). I conclude that in general the endogenous correlated equilibrium c
oncept is a more appropriate solution concept for noncooperative game
theory than the less general Nash equilibrium concept. I close by disc
ussing the relationship between endogenous correlated equilibrium and
the game solution concept called rationalizability introduced by Bernh
eim (1984) and Pearce (1984).