Until now, distributed algorithms for rational agents have assumed a-priori knowledge of n, the size of the network. This assumption is challenged here by proving how much a-priori knowledge is necessary for equilibrium in different distributed computing problems. Duplication – pretending to be more than one agent – is the main tool used by agents to deviate and increase their utility when not enough knowledge about n is given. We begin by proving that when no information on n is given, equilibrium is impossible for both Coloring and Knowledge Sharing. We then provide new algorithms for both problems when n is a-priori known to all agents. However, what if agents have partial knowledge about n? We provide tight upper and lower bounds that must be a-priori known on n for equilibrium to be possible in Leader Election, Knowledge Sharing, Coloring, Partition and Orientation.