Bandwagon effects and constrained network formation

We consider a model where players can actively form a limited number of links with other players to play a general class of size-dependent coordination games. This class of games includes multi-person binary action coordination games, minimum effort games, average opinion games, and others, and it is mainly characterized by strategic complementarities among actions. Whenever players may only support links to a relatively small number of other players, the most efficient convention will be selected, irrespective of the details of the size-dependent coordination games. When the linking constraint becomes less restrictive, the most efficient convention will still be selected, provided that the most efficient action delivers a relatively high output when played against a small group also using it. Furthermore, for the special case of size-dependent minimum effort games, the second most efficient convention may be selected.