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

Investment tournament is a type of decision problem introduced and studied in this paper. These problems involve allocation of investments among several alternatives whose values are subject to exogenous shocks. The payoff to the decision maker is a weighted sum of final values of each alternatives with weights convex in final values. (1) For the case of constant returns to scale it is optimal to allocate all resources to the most promising alternative. (2) 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 mentoring resources.