This paper studies a way to improve consistency of states in a ball game typed DVE with lag, in P2P architecture. We also study how to control shared objects in real-time in a server-less network architecture. Specifically, a priority field called Allocated Topographical Zone (AtoZ) is used for P2P typed DVE. In a critical case (i.e. inconsistent phenomena), a stricter ownership determination algorithm, called dead zone is introduced. Moreover, we propose the method to get rid of a critical case for P2P multi-player virtual ball game. By using proposed method, a robust and effective scheme is achieved for a virtual ball game. As an example of the application, a real-time networked multi-player air-hockey is implemented for evaluation of validity of proposed method. Keywords DVE (Distributed Virtual Environment), P2P (peer-to-peer), AtoZ (Allocated Topographical Zone), Count Down Protocol (CDP), Critical Case