Whom can you trust? Reputation and cooperation in networks

Community enforcement is an important device for sustaining efficiency in some repeated games of cooperation. We investigate cooperation when information about players' reputations spreads to their future partners through links in a social network that connects them. We find that information supports cooperation by increasing trust between players, and obtain the 'radius of trust': an endogenous network listing the potentially cooperative relationships between pairs of players in a community. We identify two aspects of trust, which relate to the network structure in different ways. Where trust depends on the shadow of punishment, players are trusted if others can communicate about them. This is linked to 2-connectedness of the network and the length of cycles within it. Where trust relates to knowledge of a player's type, players are trusting if they are more likely to receive information through their network connections. Both aspects of trust are linked to new centrality measures that we construct from the probabilities of node-to-node information transmission in networks, for which we provide a novel and simple method of calculation.