This paper proposes a novel kind of multi-operator multi-robot(MOMR) teleoperation systems - the competitive teleoperation system. Compared with the conventional collaborated MOMR teleoperation system, features and properties of the competitive teleoperation system are presented. Futhermore, major concerns of research and development for this kind of systems are discussed subsequently. Finally, telegame, a kind of Internet-based competitive teleoperation systems, is built as the prototype to support the future research on this aspect and some experimental results are presented to support the discussion.