No, Ohio State does not play anyone for any trophy. The closest thing to a trophy in an Ohio State/Michigan game came during the 1897 matchup, called "The Game," after which a helmet was exchanged. Ohio State is the only Big Ten school that does not have a trophy game against a conference opponent, and they have been the only school to meet this criteria since joining the Big Ten in 1950.
The Ohio State Buckeyes and Michigan Wolverines do not play for a trophy in their rivalry game.
the victory bell
Michigan beat Ohio St. 80-70.
There are at least six players that I recall who were born in Ohio, did not play for the Buckeyes and won the award. They would be Larry Kelley (Yale), Frank Sinkwich (Georgia), Dick Kazmeir (Princeton), Roger Staubach (Navy), Charles Woodson (Michigan) and Desmond Howard (Michigan).
Archie Griffin played at Ohio State and won the Heisman Trophy twice.
No, he played college ball at USC and won the Heisman Trophy. And lost to Ohio State.
Michigan Wisconsin and Illinois
The Cleveland Indians (MLB) and the Cincinnatti Bengals (NFL) play homes games in the state of Ohio. The Indians play in Cleveland, Ohio and the Bengals play in Cincinnatti, Ohio. The Chicago Bears play their home games in Chicago, Illinois and the Detroit play their home games in Detroit, Michigan.
The first ever game in the Ohio State/Michigan rivalry was played at Regents Field in Ann Arbor in 1897 with Michigan winning 34-0. At the time, Regents Field held about 800 fans.
Both teams have had many players play in the NFL Pro Bowl.
Since 1993, Penn State and Michigan State play annually for the Land Grant Trophy. With Penn State's 42-14 win in 2009, Penn State has a 13-4 record against Michigan State in this rivalry. Michigan State's last win was in 2007.
Hockey is one sport where teams play for the Champions Trophy.