Cheating by Duplication: Equilibrium Requires Global Knowledge.

Distributed algorithms with rational agents have always assumed the size of the network is known to the participants before the algorithm starts. Here we address the following question: what global information must agents know a-priori about the network in order for equilibrium to be possible? start this investigation by considering different distributed computing problems and showing how much each agent must a-priori know about $n$, the number of agents in the network, in order for distributed algorithms to be equilibria. We prove that when $n$ is not a-priori known, equilibrium for both knowledge sharing and coloring is impossible. provide new algorithms for both problems when $n$ is a-priori known to all agents. further show that when agents are given a range in which the actual value of $n$ may be, different distributed problems require different such ranges in order for equilibrium to be possible. By providing algorithms that are equilibrium on the one hand and impossibility results on the other, we provide the tight range in which equilibrium is possible but beyond which there exist no equilibrium for the following common distributed problems: Leader Election, Knowledge Sharing, Coloring, Partition and Orientation.