Ranking friends

We investigate the scope for cooperation in a community engaged in repeated interactions. Players seek the help of others and approach them sequentially according to some fixed order. This defines a ranking profile: a list for each player describing the order in which he approaches other players for help. We study the ranking profiles that are most effective in sustaining cooperation in equilibrium. It turns out that these are the profiles that spread the costs of helping equally. We provide a characterization of these socially optimal profiles that holds across all (generic) games, i.e., that does not make reference to the game parameters, in terms of a global balance property. We also study the socially optimal profiles when only the victims punish the deviator. These profiles can be characterized in terms of a more demanding local balance property.