Another option is to mobilize archers to pepper their rear. Either way the basis of warfare is to encircle, either full or half but half at least, and engage to destroy maximally or enforce their rout. Full encirclement allows maximum destruction of the enemy as routing is mostly negated.
Perhaps, with infantry units broadened to apply detailed unit flanking, you could lure their pikemen to the centre and apply overall half encirclement as if to pocket them. Their pikemen's utilization necessitates more than mere cavalry.
There are thus different effective ways to perish the foe. I suggest using combined forces instead of just cavalry: infantry, archers, cavalry, artillery --> you will find it highly efficient.
EDIT: I would not suggest bribes, even if you have vast sums of money. Simple adaptation to their pikemen's destruction will save you much and enables even greater fielding of your armies.
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