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Balancing communication workloads is a perennial performance issue in the area of Distributed Virtual Environments (DVE). The stringent time constraints of Multiplayer Online Games (MOG) complicate efforts to effectively distribute the networking load amongst servers. This issue becomes ever more exacting, when we move towards a fully Peer-to-peer virtual world (P2P-VE). We are consequently forced to factor in the limited capabilities of ordinary peers in the network. Traditional MOGs have been built on the client-server (CS) paradigm and the industry brute-force approach of over-provisioning resources is both inelegant and non-resilient in the face of failures. Moving such systems onto P2P architectures mitigates these drawbacks significantly. Our recent application of three-dimensional Voronoi Diagrams (3D-VD) onto P2P-VEs has further introduced desirable load-balancing properties in such systems. This is due to the novel use network capacity as the metric for the 3rd dimension and the subsequent use of the 3D-VD to intelligently appoint dynamic game-play arbitrators from amongst the peer population. This short paper is a preliminary report on the load-balancing properties seen in our extensive simulations. It is shown how this approach is able to appropriately distribute load in a variety of network configurations and peer populations. Thus, the performance of the collaborating peers is enhanced, ultimately leading to better game-play experience.