First-hand information for everyone
This paper studies when competitive markets work well in economies where people’s consumption affects others through multiple kinds of social ties. The authors model an economy with several goods and with externalities—effects that one person’s consumption has on others—organized by a multiplex network. A multiplex network means there are several layers of connections; each layer corresponds to one good and can have a different pattern of who influences whom. The main finding is that competitive markets can still be efficient despite these externalities, but only under clear structural conditions on the networks that generate those spillovers.
The authors build a general equilibrium model (an Arrow–Debreu economy) in which each good is tied to a network layer and people are heterogeneous in their initial endowments and in where they sit in each layer. Consumers choose how much of each good to buy subject to a budget. Markets set prices and determine who ends up with what. The paper shows that a market equilibrium exists under mild restrictions (in particular when negative externalities are not too strong) and can be unique under stronger assumptions. The authors also give a precise description of equilibrium: an agent’s consumption of a good is proportional to a network centrality measure (Katz–Bonacich centrality, which roughly counts a person’s direct and indirect influence in a network) weighted by an “effective endowment” that bundles an agent’s initial wealth and the pattern of externalities she gives and receives.
Why does the network structure matter for efficiency? The paper revisits the two classical welfare theorems. The First Welfare Theorem says a competitive equilibrium is Pareto efficient (no one can be made better off without making someone else worse off). The Second says any efficient allocation can be supported as a competitive equilibrium after a suitable redistribution of endowments. Here those theorems hold if and only if a condition called “centrality parallelism” is satisfied: for every pair of goods, the vectors of unweighted network centralities across people must be proportional. Two practical sufficient cases are identified where this condition holds: either every network layer is regular (each person has the same number of links in that layer) or every good shares the same network of links. If the condition fails, the competitive equilibrium is not Pareto efficient and the authors construct explicit Pareto-improving reallocations.
The paper also quantifies how large the inefficiencies can be. It introduces a utility-based efficiency loss (the gap between competitive-market welfare and the Pareto frontier) and a coefficient of resource utilization (CRU). The utility loss can be expressed using the Kullback–Leibler divergence, a measure of difference between two weight vectors that arise endogenously in the model. The CRU admits bounds that depend on how much the layer-specific weight vectors vary across goods. The authors further show how redistributions of endowments affect prices and welfare: pure transfers without changing total endowment can change equilibrium prices because transfers alter network interactions across goods.
Finally, the paper studies a policy that can restore efficiency: a Lindahl equilibrium, which uses personalized prices to make people face the full social costs and benefits of their consumption. While such personalized pricing can re-establish Pareto efficiency, it need not make everyone better off. In particular, highly central agents who benefited from unpriced externalities in the competitive equilibrium might be worse off under Lindahl pricing. Important caveats include model assumptions needed for the existence and uniqueness results (for example, sufficiently small negative externalities and interior equilibria in some proofs) and the fact that the efficiency of markets depends sensitively on the detailed topology of the multiple networks. The paper gives a clear set of structural conditions that determine when markets succeed or fail in the presence of networked externalities.