We analyze ways by which people decompose into groups in distributed systems. We are interested in systems in which an agent can increase its utility by connecting to other agents, but must also pay a cost that increases with the size of the system. The right balance is achieved by the right size group of agents. We formulate and analyze three intuitive and realistic games and show how simple changes in the protocol can drastically improve the price of anarchy of these games. In particular, we

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... dentify two important properties for a low price of anarchy: agreement in joining the system, and the possibility of appealing a rejection from a system. We show that the latter property is especially important if there are some pre-existing constraints regarding who may collaborate (or communicate) with whom.