Neither can "outsmart" the other without outsmarting himself. [fact]
In this game there is a compelling problem of coordination; each player can win only if he does exactly what the other expects him to, knowing that the other is similarly trying to do exactly what is expected of him. They must jointly find a line that in some fashion suggests itself to both of them or appeals to both of them. Neither can "outsmart" the other without outsmarting himself.
Thomas C. Schelling, The Strategy of Conflict, loc. 235