Credit networks are an abstraction for modeling trust among 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. We find strong positive network formation results for the simplest theoretical model. When each agent trusts a fixed set of other agents and transacts directly only with those it trusts, all pure-strategy Nash equilibria are social optima. However, when we allow transactions over longer paths, the price of anarchy may be unbounded. On the positive side, when agents have a shared belief about the trustworthiness of each agent, simple greedy dynamics quickly converge to a star-shaped network, which is a social optimum. Similar star-like structures are found in equilibria of heuristic strategies found via simulation studies. In addition, we simulate environments 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. Overall, we find that networks formed by self-interested agents achieve a high fraction of available value, as long as this potential value is large enough to enable any network to form.

We present a novel approach for identifying approximate role-symmetric Nash equilibria in large simulation-based games. Our method uses neural networks to learn a mapping from mixed-strategy profiles to deviation payoffs—the expected values of playing pure-strategy deviations from those profiles. This learning can generalize from data about a tiny fraction of a game’s outcomes, permitting tractable analysis of exponentially large normal-form games. We give a procedure for iteratively refining the learned model with new data produced by sampling in the neighborhood of each candidate Nash equilibrium. Relative to the existing state of the art, deviation payoff learning dramatically simplifies the task of computing equilibria and more effectively addresses player asymmetries. We demonstrate empirically that deviation payoff learning identifies better approximate equilibria than previous methods and can handle more difficult settings, including games with many more players, strategies, and roles.

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.

The framework of credit networks provides a flexible and robust model of distributed trust, based on pairwise credit allocations representing commitments to allow transactions. Since issuing credit entails risks as well as benefits, it is unclear whether self-interested and autonomous agents will form viable credit networks. We tackle this question through an extensive simulation-based game-theoretic analysis of a 61-node credit network formation scenario, covering eight environments varying on information and cost-benefit parameters. We find that viable credit networks form in equilibrium given sufficiently high transaction value, or sufficiently low default risk. Although the amount of credit issued in equilibrium is significantly lower than in the social optimum, as is the social welfare achieved, this difference diminishes proportionally as the environment becomes more favorable overall.

We exploit player symmetry to formulate the representation of large normal-form games as a regression task. This formulation allows arbitrary regression methods to be employed in in estimating utility functions from a small subset of the game's outcomes. We demonstrate the applicability both neural networks and Gaussian process regression, but focus on the latter. Once utility functions are learned, computing Nash equilibria requires estimating expected payoffs of pure-strategy deviations from mixed-strategy profiles. Computing these expectations exactly requires an infeasible sum over the full payoff matrix, so we propose and test several approximation methods. Three of these are simple and generic, applicable to any regression method and games with any number of player roles. However, the best performance is achieved by a continuous integral that approximates the summation, which we formulate for the specific case of fully-symmetric games learned by Gaussian process regression with a radial basis function kernel. We demonstrate experimentally that the combination of learned utility functions and expected payoff estimation allows us to efficiently identify approximate equilibria of large games using sparse payoff data.