- Multi-agent systems usually address one of two pure scenarios, completely competitive agents that act selfishly, each agent maximizing its own gain from the interaction or multiple agents that operate cooperatively in order to achieve a common goal. The present paper proposes a paradigm for multiple agents to solve a distributed problem, acting partly cooperatively and keeping a limited form of their self-interest. The proposed framework has multiple agents solving an asymmetric distributed constraints optimization problem (ADCOP), where agents have different personal gains from any mutual assignment. Three modes of cooperation are proposed--Non-cooperative, Guaranteed personal gain, and λ- cooperation (where agents' willingness to suffer relative loss is parametrized by λ). The modes of cooperation are described, as well as their realization in search algorithms.