The true positive rate gives the proportion of actual positives which are correctly identified as such. (Higher is better)
The false positive rate gives the proportion of falsely identified positives amongst all actual negatives. (lower is better)
Obviously, the most right curve (combined Joint Baysian) is worst, because for a fixed true positive rate it has always the highest false positive rate.
But how would one decide if the red or the black curve is better? Isn't there the need of a "cost" of false positives / negatives to decide that? What information can I derive from such diagrams?