Anticipation

In game theory one presumes that the opponent is as rational as oneself.  It is clear that Hannibal did not make that presumption. 

A fundamental ingredient in a strategy is a judgment or anticipation concerning the thoughts and/or behavior of others.  The simplest way of looking at Cannae is that Hannibal surrounded, or enveloped, the Romans.  But that is incomplete, for the Roman legions were the more mobile infantry on that field.  Actually, the legions were enticed into becoming enveloped, enticed into a trap, their own mobility, courage, and even initiative turned against them.   The very essence of Cannae was that the bars of the trap--the compression of the legions' ranks--were forged, in part, by the Romans' own vigorous responses to Hannibal's enticements. 

In game theory one presumes that the opponent is as rational as oneself.  It is clear that Hannibal did not make that presumption.  However, individually rational the Romans might have been, he saw the Roman army as an organization with a history, traditions, doctrine, and standardized training.  Furthermore, that organizations leaders had identifiable motivations and biases.  Some of the Roman leaders were known to be proud and a bit impetuous.

Hannibal knew these things because Carthage had fought Rome ten years earlier and came to understand its military system.  Also, part of the Roman behavior at Cannae was predictable because Hannibal had worked to shape it, raiding Varro's camp the night before, angering and embarrassing the consul in front of his troops, pushing him to seek immediate battle.  Finally, elements of Roman behavior were predictable because the battle developed quickly, giving the Romans little time to study the situation and no time to learn new lessons and alter their methods.

ACTION POINT: Don't presume, anticipate and study and know your competition.