Constrained Credit Networks
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The Credit Network is a model for transactions across a network of agents based on bilateral trust between agents. Credit Networks capture many aspects of traditional currencies as well as new virtual currencies and payment mechanisms. In a credit network, if an agent defaults, every other node that trusted it is vulnerable to loss. Alternatively, in a cryptocurrency context, securing a payment channel requires putting capital into escrow to guarantee against default. In this paper, we introduce constraints that bound the total amount of loss that the rest of the network can suffer if an agent (or a set of agents) were to default. We show that these constraints preserve two important aspects of credit networks. The first is route independence: if there are multiple trust-paths over which a transaction can clear, then it does not matter which one is used. The second pertains to liquidity (i.e. the fraction of transactions that succeed): given a symmetric transaction matrix, any achievable vector of net "credit balances" of the agents is equally likely. This technical property allows us to extend the original analysis of liquidity in credit networks to the constrained case. Surprisingly, aggregate borrowing constraints greatly simplify the analysis and achieve the optimal tradeoff between liquidity and the number of trust-edges.
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