Ouji-sama Game (KIRISHIMA Rira)

From MangaHelpers:

Takahashi Kiji is an attractive, popular, student council president, but he and his two closest friends are bored. Kiji comes up with a game, "The Prince Game." The goal is to bring the worst girl ever to his birthday party in a month. Kiji begins trying to romance the friendless, round-shouldered, weepy Asahi Mabi, who has just been through a harsh breakup. To his surprise, Mabi does not immediately swoon into his arms. Instead, she seems to be a human being, with her own thoughts and goals. She is uncomfortably good at seeing through some of his act. Seducing Mabi requires getting to know her, which is dangerous when his intention is for her to end up in tears...