I think in round 1, egoistic or not, its always better for everybody to put 1,(reply>), If everybody puts 1, the prize is 100/5 = 20 dollars, so everyone gets on average 4 dollars. But if everybody puts 1 except for one guy putting 20. The prize will be 100/24 = 4,16 and that guy has a 20/24 = 5/6 chance of winning. So on average, the one who puts 20 will get 5/6 × 4,16 = 3,472 dollars. 3,472 is less than 4. So it's just mathematically always better for everybody to put 1.