HELPING AND SABOTAGING IN TOURNAMENTS

A two-stage, two-person tournament is discussed, in which each player can influence the other one at the first stage by choosing help, sabotage or no action. At the second stage, the players choose effort to win the tournament. Helping and sabotaging have two effects — they influence the likelihood of winning (likelihood effect) and they determine the equilibrium efforts and, therefore, effort costs (cost effect). Depending on the interplay of the two effects, diverse types of equilibria are possible. In particular, if the cost effect dominates the likelihood effect (i.e., both players concentrate on minimizing effort costs), two asymmetric equilibria will coexist in which one player helps his opponent, whereas the other one chooses sabotage and vice versa.