Children in the beauty contest game : behaviour and determinants of game performance

Abstract

This study investigates the behaviour of children aged 8-11 in a beauty contest game with ten repetitions. We observe that choices convergence towards the unique Nash equilibrium over time. Using data on children’s elicited beliefs about the actions of their opponents, we find a discrepancy between choices and these beliefs. Besides the general description of behaviour, we apply the model of depth of reasoning, and learning direction theory. In earlier repetitions of the game, choices exhibit on average lower degrees of reasoning compared to the literature on experimental beauty contest games with adult subjects. Moreover, elicited beliefs reveal lower degrees of reasoning than the actual choices. Throughout the game, about half of the children adjust their choices consistent with the predictions of the learning model. Once we found evidence that children are able to play a beauty contest game, we study potential determinants of the game performance. There is a significant relationship between the understanding ratings of external observers and performance in the game. Further, while cognitive ability is not relevant, empathy skills appear to be a significant determinant. Lastly, we investigate the significance of having stated accurate beliefs and best-responding to them. Most children fail to best respond to their stated beliefs and those who did, win relatively fewer times if their beliefs were inaccurate. Finally, we complement the analysis with a sample of adults who played the same beauty contest game. The general behaviour of adults are not far from those of children, however, adults converge to the Nash equilibrium earlier in the game. Similar to children, we observe a discrepancy between stated beliefs and choices. In the beginning of the game, adults exhibit, on average, higher degrees of reasoning than children in terms of choices. Around half of the adults show behaviour in support of the learning model, although the percentage is slightly lower than that of children. We found no evidence that empathy is related to game performance as opposed to children, and cognitive ability remains uncorrelated. Adults best respond to their stated beliefs more often than children, such a strategy improves the winning frequency in the game as long as the beliefs are accurate.