Modelling the Optimal Strategies of Fertiliser Application Using the Game-Theoretic Approach

This paper is a case study which describes the application of game-theoretic approach in resource management with specific emphasis on developing optimal strategies of phosphorus applications for soil fertilisation. The approach adopted allows resource managers to consider not only competitive strategies, which were treated as the Nash equilibrium game solutions, but also 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 parametrisation. 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.