Advanced Topics in Machine Learning and Algorithmic Game Theory Fall semester , 2011 / 12 Lecture 8 : Information Cascading

Consider a game of drawing balls from a bucket. The game manager tosses a secret coin. If the outcome is heads, the manager places 3 red balls and 2 white balls, and vice versa if the outcome is tails. Each player in his turn draws a ball from the bucket, secretly and at random, and has to announce (to all other players) his guess of the outcome of the original toss. Now, suppose that the rst few players saw red balls and declared 'heads'. The rst player to see a white ball, will attribute it to chance, and, given the short sequence of red balls before her draw, she will continue to declare 'heads'. The next player has no indication that any white balls were drawn, and thus even if he too will draw a white ball he will surely declare 'heads', and so on. We see that even if that vast majority of players draw white balls, they will all beleive that there is a majority of red balls, because of a small number of draws at the beginning of the game.