Dynamic Beauty Contests: Learning from the Winners to Win?

We build a dynamic game consisting of a continuum of players to investigate the eect of previous winners ' actions on the spreadings of subsequent players ' actions. In each stage, besides the private signal, each player also observes actions taken by the winners of all previous stages as public signals. A unique equilibrium of the game is found and characterized. We then dene variances of three forms of gap: variance of the gap between the average play and the underlying fundamental value, variance of the gap between a generic player's action and the average play, and the variance of the gap between a generic player's action and the winner's play. By checking their dynamics in the equilibrium, it is shown that the accumulation of private signals always reduces the rst variance and the accumulation of the public signals always reduces the second variance. However, the accumulation of public signals reduces the rst variance if and only if the public signals are suciently precise compared to the private ones, and the accumulation of private signals reduces the second variance if and only if the private signals are suciently precise compared to th