The concept of "agent" has been used to describe many different artefacts: software programs, mobile robots, or even human beings. In a system consisting of many agents, negotiating and interacting with each other, the control of the behavior of the overall system becomes difficult. How the overall system behavior changes with respect to distributed rational decision making as a function of different utility measures is also problematic. This paper uses a wellknown matching problem to discuss options for control in a multiagent scenario. In particular, we discuss several different matching criteria and several different algorithms for resolving the matching problem. R