The Organic Computing (OC) initiative deals with new design concepts, which facilitate the development of technical systems with life-like properties such as self-organization, self-optimization and self-configuration in order to make them robust, flexible and adaptive. In this paper, we systematically investigate different interaction patterns in self-organizing agent populations using a multi-robot observation scenario from the pursuit (predator-prey) domain. We create an agent interaction scheme to demonstrate different behavioral patterns in the agent population between the fully competitive (egoistic) behavior and the fully collaborative (altruistic) behavior. In this context, we provide an optimization algorithm that is used by each agent locally to adapt its behavior to changing environmental situations. Using this algorithm, the agents explore the fitness landscape of the given problem collectively while optimizing their local performance and the system performance at the same time. Our experiments show that the system does not reach its optimum if all robots behave altruistically in the system. Rather, we get the optimum, if some of the agents in the system behave more altruistically and the others more egoistically.