Routing Mediators

We introduce a general study of routing mediators. A routing mediator can act in a given multi-agent encounter on behalf of the agents that give it the right of play. Routing mediators differ from one an- other according to the information they may have. Our study concentrates on the use of routing media- tors in order to reach correlated strong equilibrium, a multi-agent behavior which is stable against de- viations by coalitions. We study the relationships between the power of different routing mediators in establishing correlated strong equilibrium. Surpris- ingly, our main result shows a natural class of rout- ing mediators that allow to implement fair and ef- ficient outcomes as a correlated super-strong equi- librium in a very wide class of games.