What is the ruling on one who pays the manager of an oil company to ensure his bid for selling derivatives is approved, in the absence of a bidding system and with the manager requesting financial compensation?

The default ruling is that the commission requested by the manager is a forbidden bribe, and it is not permissible to pay it to him. However, if your offers are suitable and you find no alternative but to give a bribe to the manager, then the opinion may lean towards permitting its payment in such a case, and the sin would then be solely upon the manager who takes it.