Title : Heuristics and optimization: the wise man and resource renewal
Author(s) : Gisèle Umbhauer
Abstract : The paper is about a wise man, optimization and resource renewal. At time To a tribe, that lives by hunting, settles on an island for T periods. The animal to hunt is present in quantity Yo at time To and multiplies by "gamma" each period, with gamma > 1. The well-being provided by x caught animals is given by Ax-Bx² with A > 0 and B > 0, and Yo does not allow to hunt the static optimal quantity A / 2B each period. The aim of the paper is to show that a simple behavior heuristic, proposed by the tribe’s wise man, deserves more interest than classic optimization. The tribe’s wise man proposes to hunt in the first period the number of animals that ensures the possibility to hunt A / 2B animals in each subsequent period, with A / 2B( gamma -1) animals surviving the hunt each period. This simple behavior ensures a well-being that is very close to the optimal well-being. In addition, it is extremely simple, robust to any change in T, never depletes the resource unlike classic optimization, therefore respects resource renewal, biodiversity and future generations, and it is strategically stable. The paper opens on the construction of heuristics.
Key-words : Karush-Kuhn-Tucker, optimal control, heuristic, resource renewal.
JEL Classification : C61, Q20, C70
