Trying to figure out who used which kind of generl tactical scheme and when is usually pretty pointless - these sorts of things tend to develop over a long time, and it's just the first really illustrious or famous employement that shows up in them history books. Although I'll grant you it might be possible to trace the introduction and first employement of something like the Roman triplex acies system, but that's a pretty specialized one anyway...

Case in point: Ludens mentions that the "refused center" ploy was first used by Hannibal at Cannae - yet all I've read says the Athenians, by design, accident or both, actually used the same move against the Persians at Marathon. And given its nature (it may well end up getting used by accident if your center gets pushed back while the wings hold their ground and can fall on the flanks of the enemy center) it was almost certainly employed earlier too, seeing as how mass warfare is a pretty old thing...

That said, the "hammer and anvil" approach is a pretty basic trick and ought to have featured prominently in the tactical repertoire of all cultures that effectively combined infantry and cavalry. Heavy infantry of any quality, even "unarticulated" shieldwalls that cannot maneuver offensively, are by their very nature far better at holding the line and pinning an opponent in a drawn-out slugging match than any cavalry can ever hope to be; conversely cavalry, as a rule of thumb, cannot frontally attack formed, steady heavy infantry and expect any particularly illustrious results (save perhaps if it's heavy shock cavalry charging comparatively loose-order troops such as swordsmen who lack "anti-horse" weaponry such as spears). This basic equation tended to result in the heavy infantry holding the line at the center and the cavalry operating in the flanks, where their mobility was less restricted and they could hopefully be able to attack the vulnerable flanks and rear of the enemy infantry where the momentum-negating qualities of the latter weren't nearly as good. Nevermind now that lighter cavalry had a bad habit of getting badly mauled if it tried overly spirited shock action against "heavy" troops...

Alas, most of the time the opponent had his cavalry on the wings too (commanders over the millenia seem to actually have preferred to initially pit horse against horse and foot against foot in this fashion, and for pretty good reasons), so whoever gets to try and rule the flanks (or, in the absence of sufficiently solid heavy infantry as in many Medieval battles, the entire battlefield) had to first be settled between the horsemen... That's what happened at Cannae too, mind you. The heavier Carthaginian horse were able to chase their Roman colleagues from the field and pretty much run amuck behind the Roman infantry. Similarly Alexander usually had to first see off any Persian cavalry in the flanks before he could turn his Companions to help the (often rather hard pressed) phalangites in the centre.