Professor Rosemarie Nagel (ICREA-UPF and Barcelona GSE) has been thinking about the Keynesian Beauty Contest for over 20 years. In this Barcelona GSE Research Spotlight Video, Prof. Nagel explains how she uses economic experiments to test a variety of techniques designed to enable players to make better choices and improve their results in the Beauty Contest game.
History of the Beauty Contest game
The “Beauty Contest” game takes its name from a newspaper contest described by economist John Maynard Keynes in the 1930s. Entrants are shown six photographs of women and must choose the “most beautiful” one. The winners are those people who choose the most popular photograph. In other words, winning is contingent on what all the other contestants do.
Keynes reasoned that the strategy for winning such a game had little to do with fundamentals and more to do with guessing what other contestants would do. The more shrewd the player, the more complex the guessing becomes:
"It is not a case of choosing those [faces] that, to the best of one's judgment, are really the prettiest, nor even those that average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees." (John M. Keynes, General Theory of Employment Interest and Money, 1936)
Theory vs. reality
Keynes’ Beauty Contest game can be used to try to explain human behavior in a variety of scenarios, from picking stocks to standing in line for a new iPhone. However, there’s a catch: the theory behind the game is based on the assumption that players are rational.
“Not only do we need to be rational, but we have to think that the other players are rational, and so on,” Prof. Nagel explains. In this game then all have to choose the same, namely the same face, “But actual behavior is very heterogeneous. Thus it is hard to know what to do, and generally almost all people make bad decisions in these types of games, especially when they have no experience with it or when they concentrate on the theory only, or when there are multiple equilibria (here, multiple faces). The question is, how should a rational player behave in a population in which not everyone is perfectly rational?"
For this purpose, Prof. Nagel has designed an experiment for the modern Beauty Contest game (Ledoux, 1981) explained by dinosaurs (cartoon link below) and developed a model of limited reasoning, or what is now called a level-k model. "The basic idea is that a player should reason just one step ahead of the others. A level 0 player chooses a random number; a level 1 player gives best reply to level 0, the average being the midpoint of all possible choices and thus 50*2/3; a level 2 gives best reply to level 1, 50*2/3*2/3=50*(2/3)2 and so on. A game theorist being unaware of bounded rational behavior of other subjects might just play zero, like the dinosaurs do in the cartoon."
This cartoon by Ryan North explains the rules and theory of the Beauty Contest game (view full size).
Enter the economic engineer and her experiments
Professor Nagel wondered if there would be a way to help players make better decisions in the game when they are playing against other human players. To find out, she takes the game out of the realm of theory and puts it into the context of economic experiments.
In her experiments, Prof. Nagel and her collaborators tests a variety of techniques designed to enable players to make better choices and improve their results in the Beauty Contest game.
As she explains in the video, some of these experiments include:
- Giving people more experience
- Varying the time allowed
- Varying the prize for winning the game
- Giving people a hint
- Giving people feedback
- Allowing people to work in teams
In addition to performing computer experiments in the UPF LeeX Lab, Prof. Nagel, together with Giorgio Coricelli (University of Southern California), has also employed neuroscience techniques to visualize differences in brain activity when players are engaged in different levels of reasoning. Even after 20 years, she continues to find new facets of the game to explore.
“I’ve conducted lab studies, a field study via an actual newspaper Beauty Contest game, a brain study, a global game to discuss the feature of complete and incomplete information, and most recently in the newest iteration of my work on “De-anchoring Beliefs in the BCG: Keynesian Level k vs. Keynesian Sentiments” together with Jess Benhabib (NYU) and John Duffy (University of Pittsburgh), we give “precise or fuzzy signals” to subjects, helping them to make good decisions without much thinking. This is as if we de-anchor them from their own shocks (level k or random thoughts) in their heads, or in more technical terms moving from Nash equilibria to correlated equilibria," Prof. Nagel explains. “I can also see the game as a transportation devise to enter Philosophy, Literature, Religion, Neuroscience, Biology and even Art.”
The interplay of game theory and empirics
Setting aside possible applications of this work in other fields, there is still plenty of work to be done on the Beauty Contest game without straying from Economics. In fact, Prof. Nagel sees a role for experiments in areas of Economics that have not traditionally utilized such techniques.
"Experiments have historically been used in Microeconomics, but they are also important for Macro,” she says. “Take the case of the recent financial crisis. Some policy makers ignored many signs of a possible collapse maybe because these were not part of some economists’ models. The literature on the Beauty Contest game shows beautifully the interplay of game theory and empirics."
“Economists should bear in mind that game theory is for playing games, not for making predictions. However, once we have played and observed in the lab and in the field, and studied the games from all sides then we might be able to make predictions, keeping in mind that we could be unaware about important features in reality, not present in our model.”
About Rosemarie Nagel
- PhD, University of Bonn (1994)
- ICREA Research Professor at UPF
- Research Director of Experimental Economics Laboratory (LeeX) at UPF
- Teaches in Barcelona GSE masters and PhD program (GPEFM)
- A historical note on the Beauty Contest (with C. Büren and B. Frank), Joint Discussion Paper Series in Economics, 2012.
- Neural correlates of depth of strategic reasoning in medial prefrontal cortex (with G. Coricelli), Proceedings of the National Academy of Sciences (PNAS): Economic Sciences, PNAS 106:23, 9163-9168, 2009.
- One, Two, (Three), Infinity... : Newspaper and Lab Beauty-Contest Experiments (with A. Bosch-Domènech, J. García-Montalvo, and A. Satorra), American Economic Review 92, 1687-1701, 2002.
- Unraveling in Guessing Games: An Experimental Study. American Economic Review 85, 1313-1326, 1995.
- Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications. (Vincent P. Crawford, M.A. Costa-Gomes, and N. Iriberri) Journal of Economic Literature, 51(1): 5-62, 2013.