All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Bribery is to give something in order to invalidate a right or to achieve an injustice, and it is absolutely forbidden for both the one who gives it and the one who takes it, and also for the mediator between them.
As regards giving something in order to repel injustice or remove harm, and so on, then it is not the same. This is permissible for the one who gives it but forbidden for the one who takes it. Shaykh Al-Khirshi said in his commentary on Mukhtasar Khaleel: “With regard to paying money to invalidate injustice, then it is permissible for the one who gives it and forbidden for the one who takes it.” [End of quote]
Therefore, if the situation with the people in charge is as you mentioned that tender and a trade-off are not based on quality and prices and the like, and that no dealing is done with those who do not pay (a bribe) while they are able to do the work as it should be done, and the prices that they offer deserve that the job is assigned to them; in such a case there is no harm in paying a bribe to those employees if they do not conclude contracts except with those who pay a bride to them. In which case, the sin falls upon them and not upon the one who pays the bribe if he has no other alternative but to do so in order to get the contract.
Allah knows best.