# Dynamic beauty contests: Learning from the winners to win?

- 348 Downloads

## Abstract

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.

## Keywords

Beauty-contest game Public signal Winner’s action Miss Korea pageant## JEL Classification

C7 C8 D7 D8## Notes

### Acknowledgements

The author would like to thank the two anonymous reviewers for their insightful and constructive comments that greatly contributed to improving this paper. The author is grateful to Hans Haller, Éric Bahel, Joao Macieira, Zhou Yang, Shihui Ma, Fei Chen, Jiaqiang Zhuang, Kui Zhao, and the seminar participants at Virginia Tech, Huazhong University of Science and Technology, Wuhan University, Nanjing University, China Economics Annual Conference 2015, and Zhongnan University of Economics and Law, for their comments and suggestions. Nevertheless, the author is solely responsible for all remaining flaws and errors. This work has been supported by the Fundamental Research Funds for the Central Universities, HUST: 2016AB007.

## References

- Allen F, Morris S, Shin HS (2006) Beauty contests and iterated expectations in asset markets. Rev Financ Stud 19(3):719–752CrossRefGoogle Scholar
- Amador M, Weill PO (2012) Learning from private and public observations of others’ actions. J Econ Theory 147(3):910–940CrossRefGoogle Scholar
- Angeletos GM, Pavan A (2007) Efficient use of information and social value of information. Econometrica 75(4):1103–1142CrossRefGoogle Scholar
- Angeletos GM, Werning I (2006) Crises and prices: information aggregation, multiplicity, and volatility. Am Econ Rev 96(5):1720–1736CrossRefGoogle Scholar
- Angeletos GM, Hellwig C, Pavan A (2006) Signaling in a global game: coordination and policy traps. J Polit Econ 114(3):452–484CrossRefGoogle Scholar
- Bacchetta P, Van Wincoop E (2008) Higher order expectations in asset pricing. J Money Credit Bank 40(5):837–866CrossRefGoogle Scholar
- Corsetti G, Dasgupta A, Morris S, Song Shin H (2004) Does one soros make a difference? A theory of currency crises with large and small traders. Rev Econ Stud 71(1):87–113CrossRefGoogle Scholar
- Haller H, Yi M (2013) Paths of a continuum of independent random variables. Working Paper, Virginia Polytechnic Institute and State University, Department of EconomicsGoogle Scholar
- Jolliffe I (2002) Principal component analysis. Springer, New YorkGoogle Scholar
- Judd KL (1985) The law of large numbers with a continuum of IID random variables. J Econ Theory 35(1):19–25CrossRefGoogle Scholar
- Keynes JM (1936) The general theory of employment, interest and money. Macmillan, LondonGoogle Scholar
- Morris S, Shin HS (2002) Social value of public information. Am Econ Rev 92(5):1521–1534CrossRefGoogle Scholar
- Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3(1):71–86CrossRefGoogle Scholar
- Vives X (2008) Information and learning in markets: the impact of market microstructure. Princeton University Press, PrincetonGoogle Scholar
- Wang C (2013) Bailouts and bank runs: theory and evidence from tarp. Eur Econ Rev 64:169–180CrossRefGoogle Scholar