The series between Waseda and Keio, Sōkeisen (早慶戦), attracts the most attention and is greatly enjoyed by the students, not least because it causes classes at both universities to be canceled. The game is still broadcast on NHK and it is the only series played during the last week of the season (each Spring and Fall season had Soukeisen helds on the end of season since the rotation game between Waseda vs Keio only comes in the last week of the season).
The Sōkeisen actually predates the establishment of the Tokyo Big 6 League by over 20 years, beginning in 1903. The games often caused much tension between the two student bodies, often spilling out of the stadium and leading to the cancellation of games.
The addition of Meiji (1914), Hosei (1917) and Rikkyo (1921) would do little to remedy the rivalry. This state would continue until the addition of Tokyo Imperial University and the official establishment of the Tokyo Big 6 Baseball League.
The name is a combination of the two university's names first kanji characters and the character for battle or match, sen (戦). Sō, is the alternate reading of Wa (早) in Waseda (早稲田) (also from the short name, Sōdai (早大)), while Kei (慶) is the first character of Keio (慶応).
Source : Wikipedia - Tokyo Big 6 League