I've heard from a friend that citizens of The Capitol can buy tributes for various reasons.
Is this true?
If so, please provide a source and more information about this.
Mooz's answer is an excellent summary, but since it relies mainly on Wikia quotes, I thought a canon answer would also be helpful. Here's the relevant excerpt from Mockingjay (Chapter 12, page 170; emphasis mine).
"President Snow used to ... sell me ... my body, that is," Finnick begins in a flat, removed tone. "I wasn't the only one. If a victor is considered desirable, the president gives them as a reward or allows people to buy them for an exorbitant amount of money. If you refuse, he kills someone you love. So you do it."
That explains it, then. Finnick's parade of lovers in the Capitol. They were never real lovers. Just people like our old Head Peacekeeper, Cray, who bought desperate girls to devour and discard because he could. I want to interrupt the taping and beg Finnick's forgiveness for every false thought I've ever had about him. But we have a job to do, and I sense Finnick's role will be far more effective than mine.
"I wasn't the only one, but I was the most popular," he says. "And perhaps the most defenseless, because the people I loved were so defenseless."
Here's why the same didn't happen to Haymitch (same chapter, a couple of pages later):
"Is that what happened to you?" I ask Haymitch.
"No. My mother and younger brother. My girl. They were all dead two weeks after I was crowned victor. Because of that stunt I pulled with the force field," he answers. "Snow had no one to use against me."
"I'm surprised he didn't just kill you," I say.
"Oh, no. I was the example. The person to hold up to the young Finnicks and Johannas and Cashmeres."
Yes.
What you're thinking about is Finnick Odair; from the Wikia page:
In Mockingjay, it was revealed that President Snow "rented" his body out to wealthy Capitol citizens and if Finnick refused, President Snow would kill somebody he loved.".
[1]
But there is no evidence that this is common practice in The Capitol.
I would wager though that there are prostitutes in The Capitol. I base this on the fact that Panem is a derivative of Panem Et Circes[2][3], which means "Bread and Circuses". This means that the citizens of The Capitol are lavishly catered for, and distracted with entertainment - this apparently includes the use of prostitution.
Another reference I can think of is Johanna Mason, who apparently:
President Snow later killed her family after the games, because she would not agree on being prostituted, since she was a very desireable[sic] victor.[4]
President Snow has also apparently forced other victors into prostition; from his Wikia page:
He [Snow] was not hesitant to use people for his personal advantage. For example, he used Finnick and other (unknown) attractive victors and sold them into prostitution to affluent Capitol citizens. Cashmere was also one of his victims of prostitution. Snow tried to prostitute Johanna Mason as well, but she refused to go along with his plan. Because of this, he ruthlessly killed all of her loved ones, which only inflamed her hatred of him further rather than breaking her.[5]
There is an excellent article on this subject by Angel Daniel Matos, called Male Prostitution and [The Hunger Games] – The Case of Finnick Odair.