MR KEYNES’ ‘BEAUTY CONTESTS’: HOW BAD WE ARE AT GUESSING GAMES
How deep is our thinking when we try and calculate how other people will behave, for example when we make investments in financial markets? Not very, according to Professors John Duffy and Rosemarie Nagel writing in the November 1997 issue of the Economic Journal. Their experimental research into how individuals form expectations of other people’s expectations uses a game called the ‘beauty contest’. The results suggest that we tend to use a very low order degree of reasoning about other people’s behaviour even when the ‘game’ is repeated for many rounds.

Duffy and Nagel’s experiment draws on John Maynard Keynes’ insight that the behaviour of investors in financial markets is like newspaper beauty contests in which readers were asked to choose the six prettiest faces from 100 photographs. The winner was the person whose preferences were closest to the average preferences of all participants. Keynes reasoned that contest participants, like financial investors, do not choose faces (investments) that they personally find the most attractive but are instead guided by their expectations of other people’s expectations.

In the ‘beauty contest’ game, named in honour of Keynes, a group of subjects is asked to guess a number from 0 to 100. The winner is the person(s) whose guess is closest to half of either the median, the mean, or the maximum number chosen by all players. The winners are paid $20. The game is repeated several times, and subjects are informed of the results of each game. Regardless of the statistic used to determine the winning number, economic theory predicts that all players should announce zero so that everybody is a winner.

The objective of the experiment is to elicit the degree of reasoning that individuals use in forming expectations of others. Suppose, for example, that half of the mean is used to determine the winning number. An individual might reason that the mean could be no higher than 100. Therefore, the winning number could be no greater than half of 100, or 50. If this individual believed that all the others would choose 50, it would be rational for her to choose 25, approximately half of the mean. This analysis can be continued further to the point where if all individuals used an infinite degree of reasoning, they would arrive at the equilibrium where all announce zero.

Duffy and Nagel find that players tend to use a very low order degree of reasoning when forming expectations of others' expectations. For example, in the first round of the ‘half-median’ game, many subjects choose 25 or 12.5 while no one chooses 0. In the second round, after seeing that the median was say 25, many subjects will choose numbers close to 12.5 or 6.25. If the game is repeated for many rounds, the numbers chosen get closer to zero, but most players continue to use a very low order degree of reasoning.

Duffy and Nagel also find that the statistic that determines the winning number matters for how quickly players move toward the equilibrium where all announce zero. Convergence to the equilibrium is slowest in the ‘half-maximum’ game and fastest in the ‘half-median’ game.

The ‘half-maximum’ game can be thought of as a financial market where the actions of one big investor (the person choosing the highest number) create uncertainty for the other smaller investors. The ‘half-median’ game can be thought of as a market where all investors have equal influence. In forming expectations of others' expectations, players come closest to coordinating on the ‘market fundamentals’ equilibrium where all announce zero in the ‘half-median’ game, and are furthest from such coordination in the ‘half-maximum’ game.

Note: ‘On the Robustness of Behaviour in Experimental "Beauty Contest" Games’ by John Duffy and Rosemarie Nagel is published in the November 1997 issue of the Economic Journal. Duffy is Professor of Economics at the University of Pittsburgh, PA 15260, USA; Nagel is Professor of Economics at Universitat Pompeu Fabra, 132 Balmes, Barcelona 08008, Spain.

For Further information: contact RES/ESRC Media Consultant for Economics Romesh Vaitilingam on 0171-878-2919, 0117-983-9770 or mobile 0468-661095; Rosemarie Nagel on 00-34-3-542-2739 (email: nagel@upf.es); or John Duffy on 001-412-648-1733 (email: jduffy+@pitt.edu).