In Mississippi, university officials sent state gambling regulators names for a “watch list” for big bets. Iowa colleges have simply kept teaching their athletes longstanding, narrowly applied rules on sports wagering. And in Indiana and Pennsylvania, some universities flatly banned students and employees from betting on their school’s athletics events.

The rapid spread of legalized sports betting, made possible by a United States Supreme Court ruling last year, is prompting colleges and universities to grapple quickly with whether they can, or should, control a lawful activity so explicitly linked to the performances of their students.

But as more states have allowed bets and as wagers have soared — there were more than $730 million in sports bets in August, more than double the amount from a year earlier — there is no consensus among universities about how they should respond. And it is unclear whether the initial reactions will stave off any problems that critics fear might come from bets on everything from bowl games to March Madness brackets.

“Because these are fuzzy questions, and they're new questions, we’re not asserting that we've got it tacked down in all particulars,” Mitch Daniels , Purdue’s president, said in an interview as university officials labored this month over the precise wording of their new policy.