Risk Taking in Asymmetric Tournaments

A tournament is examined in which two agents with different abilities choose efforts as well as risks. According to the previous literature, the more (less) able agent should choose a low (high) risk strategy, because the first one does not want to imperil his favorable position, whereas the last one can only gain by increasing risk. We show that this is not necessarily true. Risk taking affects equilibrium efforts as well as winning probabilities. Depending on both effects diverse equilibria are possible. For example, the low and the high ability agent may both choose high risks or both choose low risks