Are you to stay with one poem, or can it be one poet?  If more than one poem, you could have the competitors complete couplets—say, “Listen, my children and you shall hear/(Respond) Of the midnight ride of Paul Revere.”  Is the game instructive or memory-driven?  A long poem, like “Ode: Intimations of Immortality” (Wordsworth) may be best.  The interactive part can be completion of a line, or matching a line with its literal or metaphorical meaning.  Pick a poem with some "meat” to it, and one you wouldn’t mind memorizing.  Then interactively, the other students can comment on it, add lines to it, or even correct your changes to it.  If you pick a poem and tell us, we can be more specific and helpful.  How about matching the last line of a Yeats poem to its title?