A Game Theoretic Approach to Sustainizability Over Sets and its application to a multi-species population model

Abstract

In this work, a theorem is first proved which presents a game theoretic formulation of a necessary and sufficient sustainizability over a set condition for a general system described by ordinary differential equations (ODEs). Then, two additional theorems are proved for the n-species Gause-Lotka-Volterra (GLV) population model, establishing necessary and sufficient sustainability and sustainizability conditions over rectangular sets. Three case studies on the May-Leonard, 3-species, GLV model are then presented to illustrate the power of the above Theorems. In two of these case studies (2 and 3), it is shown that a particular instance of the 3-species, GLV model is unsustainable but sustainizable through allowable action.