I'm looking for manga where one character "buys" another character.

That can be taken litterally, as in bought from someone like a slave, concubine, or prostitute(geisha).

Or it can mean the character was paid to enter another character's family (like be the wife/husband or child). Butler/bodyguard/servant are also good.

It doesn't have to be money that binds them either, it can be blackmail.

some good examples are:
antique romance
tokyo crazy paradise
Gerard to jacques
hapi mari

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Feed your head.

You can try these titles:

Billion Girl - pays her debt as wife
Desire Climax - pay her debts as servant
Hadashi de Bara wo Fume - same as Billion Girl
Hadashi no Aitsu - same as Desire Climax

Hope you enjoy ^^

Not exactly buying but "possession" is an important theme in these...

Reimei no Arcana - Girl is (really) unhappily "sacrificed" into marriage into the royal family of another country in order to maintain "peace".

Sakura Hime Kaden - maybe? Forced royal marriage. I don't follow this manga too much, although it's made by the great Arina.

Seirei Produce - A bad luck plagued girl comes across a guy, who says he's a god, and eventually...he ends up seeing her as his "follower". Of course, the girl doesn't want that and thinks the guy is crazy. Then trouble follows, other than the guy with his servant, forcing themselves into her life..

Now, the more money related themes..

Shinshi Doumei Cross+ - Girl gets sold into another family. Girl attends a very elite private high school. Girl joins student council and eventually learns the full truth about her past, her relationship with the council president, and........well... I can't spoil it.

Million Girl - Girl risking her money on a game... (So, not exactly character buys another character, but the girl is forced into the situation.)

Platinum Garden - Girl lives with a rich family in order to pay off debts of her late grandfather, but there's a bit more to it than what meets the eye...

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Ousama Game - sorta, aanyway
it's only an oneshot;
Butterfly Night & Lovers in the Tower that Touches Heaven - if you can still stand Kayono after what she did, this stories that do belong to her are not half bad;
Tenshi ja Nai - blackmail;
I Wish - in the description on MU it says that K "agrees to take her on as an apprentice", actually he threatens to kill her unless she becomes his assistant or makes a wish and gives him her most prized possesion in return;

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I love vampires.

First Girl
Chiro Star Project
Kuro Bara Alice more or less since

Forbidden Kiss

Although it only matters in the first 5 volumes... But since only 12 chapters were scanlated so far...

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Let's just say Tarot Cards rule.

Okane Ga Nai
it's really good but it is a somewhat harcore yaoi (depending on what you think is hardcore)

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It can't rain all the time