Efficient structure of noisy communication networks

In the canonical network model, the connections model, only three specific network structures are generically efficient: complete, empty, and star networks. This renders many plausible network structures inefficient. We show that requiring robustness with respect to stochastic information transmission failures rehabilitates incomplete, redundant network structures. Specifically, we show that star and complete networks are not generally robust to transmission failures, that circular and quasi-circular networks are efficient at intermediate costs in four-player networks, and that if either of them is efficient, then at least one of them is pairwise stable even without reallocation. Thus, incomplete, redundant networks are efficient and stable at intermediate costs.