Cyberspace is the newest domain of conflict and cooperation between states. In cyberspace, as in all other domains, land, sea, air, and space, these interactions often lead to the emergence of hegemons which are characterised by their predominant influence over global world order and all other states. We examined the emergence and collapse of hegemons in a modelled cyberspace world through the notions of power transition and power diffusion. We used Repast Simphony to construct a simple agent-based model (ABM) of a system of states interacting both competitively and cooperatively in this world. Our simple model parsimoniously captures the character of the real international system of states through simple parameters of wealth and power determining the outcome of attack or cooperation amongst pairwise interacting states. We found hegemons of global world order emerged in cyberspace as they do in the other traditional domains from models with these few parameters. And we found that hegemons, contrary to traditional understanding, are not exceptional states but merely occupy the tail of a continuous distribution of power and lifetimes. We also found that hegemony in the system depends on two perhaps unexpected parameters: the difficulty of acquiring power as wealth increases and the amount of cooperation between states. And as a consequence, we argue that cyberspace, as a power-diffuse domain where cooperation is easier than elsewhere, is less suited to the kind of hegemony we see in the traditional domains of state interaction.