I read it about a relationship of two men, where one praised the other extensively for solely his own benefit.
2 Answers
The question requests a verb: "the act of..."
The verb is "flatter". Example:
Joe flattered his boss constantly so as to win the coveted promotion.
The noun expressing the act of flattering is "flattery", as in
Flattery will get you nowhere.
In the above sentence the speaker is saying that he/she is immune to flattery.
By the way, in my experience almost no one is immune to flattery. Try flattering your boss, your date, or your banker when applying for credit; you'll be pleased with the results.
Someone who is a self-serving flatterer is a sycophant
From https://www.vocabulary.com/dictionary/sycophant:
A sycophant is a person who tries to win favor from wealthy or influential people by flattering them. Also known as brown-nosers, teacher's pets or suck-ups.
noun. a person who tries to please someone in order to gain a personal advantage
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Hi faustus, it's great that you're contributing potentially useful answers, but the system is rightly flagging them for deletion as "low-quality because of its length and content." An answer on this site is expected to be authoritative, detailed, and explain why it is correct. You can edit your answer, at the very least adding a definition for sycophant linked to the source. For further guidance, see How to Answer. :-) Commented Nov 17, 2018 at 23:29