A note on the properties of the optimal solution(s) of the Greed and Regret problem

The Greed and Regret problem is a simple model with applications in areas such as studies of crime, ultimatums, bidding, setting service levels and sales force compensation. In general, the Greed and Regret problem is not concave, and may admit several local optima. Nevertheless, the optimal solution exhibits some intuitive monotonicity properties with respect to the problem parameters. We identify a sufficient condition for uniqueness of the optimal solution, which is a generalization of the Increasing Generalized Failure Rate property developed by Lariviere and Porteus (2001).