Interbanking networks: towards a small financial world?

In a standard stylised frame derived from Diamond Dybvig, banks operate within a network of debt contracts. Working in network enables banks to decentralize a Pareto Optimal allocation while it is impossible if banks operate in isolation. However, this outcome depends on the architecture of the network which itself depends on network participant number and on the cost structure. In a general frame with no cost, two network structures only decentralize first best outcome. The first structure highlights a Small World property as banks must be bound together at a network distance that equals at maximum 2. The second structure exhibits a strict regular topology. The rise in the number of competing banks leads to a more than proportional rise in interbank lending operations. In a frame with positive cost, we prove a single architecture both minimizes aggregate costs and decentralizes first best outcome. However, this topology has little chance to emerge as it exhibits unbalanced cost sharing among players. Aggregate cost efficiency is indeed not compatible with individual cost minimization