Correlation and Authentication in Repeated Games with Network Monitoring

We study repeated games with network monitoring where players observe the moves of their neighbors. The Folk theorem holds for such a game if every feasible and individually rational payoff is an equilibrium payoff. Renault and Tomala [RT98] prove that given a network, the Folk theorem holds in Nash equilibria for every payoff function if and only if the graph is 2-connected. This paper shows that if players share correlated authentication keys, the connectivity requirement can be relaxed, i.e. the Folk theorem holds in correlated equilibria for every payoff function if and only if the graph is 2-edge-connected. The problem is also formulated in terms of communication protocol construction and the result is similar to others in the computer science literature: the distribution of private authentication keys helps reliability of communication. VERY PRELIMINARY DRAFT.