Ranking games and gambling: When to quit when you're ahead

It is common for rewards to be given on the basis of a rank ordering, so that relative performance amongst a cohort is the criterion. In this paper we formulate an equilibrium model in which an agent makes successive decisions on whether or not to gamble and is rewarded on the basis of a rank ordering of final wealth. This is a model of the behaviour of mutual fund managers who are paid depending on funds under management which in turn are largely determined by annual or quarterly rank orderings. In this model fund managers can elect either to pick stocks or to use a market tracking strategy. In equilibrium the final distribution of rewards will have a negative skew. We explore how this distribution depends on the number of players, the probability of success when gambling, the structure of the rewards, and on information regarding the other player's performance.