Dynamic beauty contests: Learning from the winners to win?

I build a dynamic game consisting of a continuum of players to investigate the effects of previous winners’ actions on the spreading 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. I then define the variances of three forms of gap: the gap between the average play and the underlying fundamental value, the gap between a generic player’s action and the average play, and 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 first variance and the accumulation of the public signals always reduces the second variance. However, the effects of accumulated public (private) signals on the first (second) variance are rather ambiguous. Based on a theoretical finding that expresses the third variance as a weighted sum of the other two, I conduct an empirical study on the Miss Korea pageant during 1994–2013. I find a descending trend in the variance of the gap between the average face and the underlying “true beauty” face over these years. Moreover, this process is accompanied by ascending trends in the other two variances, indicating that contestants’ faces have been converging to the “true beauty” overall but diverging from each other over the two decades, which is consistent with our theoretical results.