100 (because it makes the math simpler for me).
1. after the players have all settled down to picking 100 for a few rounds of the game, i change the rules slightly. i tell half the players to pick a number 10% higher than the average pick, and tell the other half to pick a number 10% less than the average pick. (and i change the rewards accordingly, and they all get to hear me tell them all this.) what happens next? i don't know. but my guess is that half of them will pick 110, and the other half will pick 90, so the average stays at 100. dear reader: 