Learn Russian: Руководство не уступает давлению конкурентов. - The management does not yield to the pressure of competitors.

The verb уступает (from уступать, meaning to yield or give in) directly governs the Dative case for the thing or person you are yielding to. This is known as the Dative of Submission. You do not need a preposition; the Dative case alone expresses what is receiving the submission.

Does уступать only apply to abstract concepts like pressure or demands?

No, it is also used for physical situations. A very common everyday use is giving up your seat to someone on public transport, like уступить место пожилому человеку (to give up a seat to an elderly person). Both abstract and physical uses require the Dative case for the receiver.

Why is the word for competitors, конкурентов, in the Genitive case?

It shows possession or attribution, equivalent to the English word of. While давлению is Dative because of the verb, конкурентов is Genitive plural because it directly modifies давлению (the pressure of the competitors). Case requirements do not chain; each word's case is determined by its immediate grammatical parent.

Since management refers to multiple people, could we use the plural verb уступают?

No, in Russian, collective nouns like руководство are strictly grammatically singular. Because руководство is a neuter singular noun, it must take the singular verb form уступает, regardless of how many people actually make up the management team.