Urusei Yatsura

An alien race known as the Oni arrive on Earth with the intention of invading the planet. Instead of taking over the planet by force, the Oni give humans a chance to fight for the rights to the planet by competing in a competition. The competition is a variant of the game of tag (literally "the game of the Oni" in Japanese), in which the human player must touch the horns on the head of the Oni player within one week. The computer selected human player is Ataru Moroboshi, a highly lecherous, very unlucky and stupid high school student from the Japanese city of Tomobiki, and the Oni player is Princess Lum, daughter of the leader of the attempted Invasion.

Despite his initial reluctance to take part in the competition, Ataru becomes extremely interested in the game when he meets Lum. When the competition begins, Lum surprises everyone by flying away and Ataru finds himself unable to catch her. Before the last day of the competition, Ataru's girlfriend Shinobu Miyake encourages Ataru by pledging to marry him if he wins. On the final day of the competition, Ataru wins the game by stealing Lum's bikini top, which prevents her from protecting her horns in favor of protecting her modesty. In celebrating his victory, Ataru expresses his joy at being able to get married; however, Lum misinterprets this as a proposal from Ataru and accepts on live television. Despite the misunderstanding, Lum falls in love with Ataru and moves into his house.