Hockey Fans vs. the Band
Every time an opposing player is penalized at a University of Michigan home hockey game, the student fans begin chanting long strings of obscene epithets. After the first few times this happened, the band began playing loud music (lots of drums) to drown this out. This is a repeated game, with the students as the first-mover (strategy: chant/no chant), and the band a follower (strategy: play/don’t play).
By now, with many rounds (penalties) having occurred during games, other fans can’t hear the students at all; the second they begin to chant, the band begins playing.
This is not a desirable equilibrium for the students. What should they do to have some impact (assuming they aren’t just chanting to hear themselves)? They will always be first-movers, which is a disadvantage in this case; but perhaps if they randomize chanting (chant only at random penalties) they can surprise the band and have a few seconds of audible chanting.
Of course, after a while the band will simply start playing at every penalty, so randomized chanting won’t work either. I think the equilibrium is that the students will never be heard. Is there any hope for them?