Strategic formation of credit networks

Credit networks are an abstraction for modeling trust between agents in a network. Agents who do not directly trust each other can transact through exchange of IOUs (obligations) along a chain of trust in the network. Credit networks are robust to intrusion, can enable transactions between strangers in exchange economies, and have the liquidity to support a high rate of transactions. We study the formation of such networks when agents strategically decide how much credit to extend each other. When each agent trusts a fixed set of other agents, and transacts directly only with those it trusts, the formation game is a potential game and all Nash equilibria are social optima. Moreover, the Nash equilibria of this game are equivalent in a very strong sense: the sequences of transactions that can be supported from each equilibrium credit network are identical. When we allow transactions over longer paths, the game may not admit a Nash equilibrium, and even when it does, the price of anarchy may be unbounded. Hence, we study two special cases. First, when agents have a shared belief about the trustworthiness of each agent, the networks formed in equilibrium have a star-like structure. Though the price of anarchy is unbounded, myopic best response quickly converges to a social optimum. Similar star-like structures are found in equilibria of heuristic strategies found via simulation. In addition, we simulate a second case where agents may have varying information about each others' trustworthiness based on their distance in a social network. Empirical game analysis of these scenarios suggests that star structures arise only when defaults are relatively rare, and otherwise, credit tends to be issued over short social distances conforming to the locality of information.