Selection tournaments, sabotage, and participation

This paper studies sabotage in tournaments with at least three contestants, where the contestants know each other well. Every contestant has an incentive to direct sabotage specifically against his most dangerous rival. In equilibrium, contestants who choose a higher productive effort are sabotaged more heavily. This might explain findings from psychology, where victims of mobbing are sometimes found to be overachieving. Further, sabotage equalizes promotion chances. The effect is most pronounced if the production function is linear in sabotage, and the cost function depends only on the sum of all sabotage activities: in an interior equilibrium, who will win is a matter of chance, even when contestants differ a great deal in their abilities. This, in turn, has adverse consequences for who might want to participate in a tournament. Since better contestants anticipate that they will be sabotaged more strongly, it may happen that the most able stay out and the tournament selects one of the less able with probability one. I also study the case where some contestants are easy victims, i. e. easier to sabotage than others.