This paper studies the way to improve consistency of states in a ball-game typed Distributed Virtual Environment (DVE) with lag, in peer-to-peer (P2P) architecture. That is, we are studying how to reduce in real-time the difference of states between the participating terminals in a virtual ball game caused by transmission lag or update interval. We are also studying 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 in P2P for DVE. In a critical case, defined as inconsistent phenomena between the peers, caused by the network latency, a stricter ownership determination algorithm, called dead zone is introduced. Concession parameter is used to reduce the possibility of such a case. By using these protocols in combination, a robust and effective scheme is achieved for a virtual ball game and these protocols ware extended for multi-player game. As an example of the application,...