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Credit networks represent a way of modeling trust between entities in anetwork. Nodes in the network print their own currency and trust each other fora certain amount of each other's currency. This allows the network to serve asa decentralized payment infrastructure---arbitrary payments can be routedthrough the network by passing IOUs between trusting nodes in their respectivecurrencies---and obviates the need for a common currency. Nodes can repeatedlytransact with each other and pay for the transaction using trusted currency. Anatural question to ask in this setting is: how long can the network sustainliquidity, i.e., how long can the network support the routing of paymentsbefore credit dries up? We answer this question in terms of the long termfailure probability of transactions for various network topologies and creditvalues.  We prove that the transaction failure probability is independent of the pathalong which transactions are routed. We show that under symmetric transactionrates, the transaction failure probability in a number of well-known graphfamilies goes to zero as the size, density or credit capacity of the networkincreases. We also show via simulations that even networks of small size andcredit capacity can route transactions with high probability if they arewell-connected. Further, we characterize a centralized currency system as aspecial type of a star network (one where edges to the root have infinitecredit capacity, and transactions occur only between leaf nodes) and computethe steady-state transaction failure probability in a centralized system. Weshow that liquidity in star networks, complete graphs and Erd\"{o}s-R\'{e}nyinetworks is comparable to that in equivalent centralized currency systems; thuswe do not lose much liquidity in return for their robustness and decentralizedproperties.

Liquidity in Credit Networks: A Little Trust Goes a Long Way