This paper aims to study how to gain the consistency of the state in a DVE (Distributed Virtual Environment) with lag, under the condition of peer-to-peer architecture. That is, we study how to reduce in real-time the difference of the DVE state between peers caused by transmission lag or update interval, and how to control the shared object in the online field game. Specifically, the priority field called Allocated Topographical Zone (AtoZ) and Mutual Prediction Protocol is used in peer-to-peer DVE. Moreover considering the critical case (the inconsistent phenomena) caused by the network latency between peers, stricter ownership determination algorithm called the dead zone is introduced. Using these three protocols in combination, a robust and effective scheme is realized. As an example of the application using the protocols, a real-time networked air-hockey is implemented for evaluation of the influence on interactivity and consistency.