How would world history shape up had Rome surrendered after the battle of Cannae?
The carthagenian peace planned for Rome was to deconstruct her as hegemon in Italy and make the other city states clients of Carthage.
Rome would probably have challenged such a system a generation later and began a reconquest. The Roman system of conscription, the farmer soldier, the roman concept of warfare so different than the carthagenian one, the roman population and ability to replace losses and many other advantages was so overwhelming that Cartaghe had no chance of ever defeating Rome in the long run.
Hannibal was much like Japan in WW2, in its war agains the US, failing to undestand that the opponent had an existential view of warfare. A merchant state like Carthage could not compete with a pseudo-national state like Rome.