Investment Tournaments: When Should a Rational Agent Put All Eggs in One Basket?∗

We introduce and study a class of decision problems which we call “investment tournaments.” The problems of this class involve gradual allocation of investments among several alternatives whose values are subject to exogenous shocks. The payoff to the decision-maker is determined by the final values of the alternatives. We show that in a broad range of situations it is optimal for the decision-maker to allocate all resources to the most promising alternative, hence diversification is suboptimal. In particular this is the case when the decision-maker’s payoff is given by the weighted sum of the final values of alternatives or their convex transforms. In tournaments for a promotion the agents would rationally choose to put forth more effort in the early stage of the tournament in a bid to capture a larger share of employer’s investment, such as mentoring.