Self-selection in tournaments: The case of chess players

• Who self-selects into a tournament with entry cost?
• Empirical study of this question in the case of a chess tournament.
• Prizes in this tournament are high.
• It is assumed that chess ability is only partially observed by the econometrician.
• Theoretically, high rated players should participate more than low rated ones. This is confirmed by the data.
• High rated players participate even when they have a negative ability shock. Low rated players stop participating when they have a negative ability shock. Consequently, on average, low rated players are expected to perform better than high rated players. This is confirmed by the data.

We consider a simple tournament model in which individuals auto-select into the contest on the basis of their commonly known strength levels, and privately observed strength-shocks (reflecting temporary deviations from observed levels). The model predicts that the participation rate should increase with the player's observed strength, and the total awarded prize amount. Furthermore, under certain conditions self-selection implies that participants with high observed strength levels have smaller expected strength-shocks than those with low levels. Consequently, the latter should play better than predicted and the former worse (given their observed strength). These predictions are confronted with data from a large and high-prize chess tournament held in the USA. This tournament is divided into different sections, with players being able to play in the section to which their current chess rating (observed strength) belongs. As predicted, we find that within each section the participation probability increases with chess rating and prize amounts, and players with a relatively low (resp. high) rating are indeed the ones who have a better (resp. worse) relative performance.