A Game Theoretic Approach for Selecting Optimal Strategies of Fertiliser Application

The paper describes the application of game theoretic approach in resource management with specific application to development of optimal strategies of phosphorus applications for soil fertilisation. This approach allows resource managers to consider not only competitive strategies, which were treated as the Nash equilibrium game solutions but the strategies which imply cooperation between farmers. These strategies were modelled as the cooperative Pareto optima of the game. The objective function of the game has been developed in order to reflect both economic advantages of phosphorus applications and the environmental losses associated with these applications expressed as dollar values. The paper presents algorithms for finding competitive and cooperative solutions of the game for the particular case when no time scheduling is included in the game parametrization. The results obtained in the paper showed that the cooperative solutions lead to much lesser environmental impacts than that in the case of non-cooperative strategies.