Your Title

The memory process Γ (t) is an ergodic Markov Chain on S . We emphasize that S is simply the set of "feasible states", where the values in U We next show that Γ ( t) on S is an ergodic chain. We conclude that Γ ( t) on S is an ergodic Markov chain by definition. G is a connected graph, and that the communication protocol is proper. G. Therefore, using the properness of the communication protocol, there is a positive probability that for any n,m, a message from player m can reach player n, containing the reward of player m (that is always known to it).