The behaviour of multiple agents who utilise one common resource will be investigated in this thesis, where different growth models for the resource are taken into account. The agents' utility depends on the stock of the resource, their extraction rate and their technological level, which can be increased with investments. The influence of how much one agent is future-oriented will be the key point for the optimal control strategies. The main focus is on the one agent problem, how the optimal solution of this one agent changes if a second agent is introduced, and at last, how the optimal outcome of these two agents can be increased, if instead of a full competition on the market the agents mutually agree on a certain commitment strategy in order to jointly extract the resource optimally. It will turn out that in any case a certain commitment is of benefit for both agents and will increase their output compared to the non-commitment strategy. Solutions will be obtained by applying Pontryagins Maximum Principle and the concept of Nash equilibria in a differential game setup and the obtained numerical solutions for the two agent cases are explicitly given and analysed.