What is the ruling on a sales representative taking a commission in exchange for motivating salespeople from other companies to increase their purchases of products from the company he works for, knowing that these incentives are given without the employers' knowledge?

It is not permissible to give commissions or incentives to salespeople in other companies for selling your company's products without the approval of their employers, because this falls under forbidden gifts to employees. If the employer does not approve, you must clarify the unlawfulness of these incentives to your company's officials, for there is no obedience to a creature in disobedience to the Creator.

As for the ruling on the commission you receive: if it is in exchange for incentivizing workers in this forbidden manner, then it is not permissible. However, if it is for your sale of your company's products to those companies, the majority of scholars stipulate that the commission must be a known amount, while some scholars permit the wage to be a percentage of the profit. This latter opinion may be adopted, so it is permissible for you to take this commission if it is not contingent on an act that is impermissible according to Sharia.