This note contains complementary information to the paper Staudigl and Steg

(2014). We present a martingale characterization of continuation payoff processes in a

class of repeated games with imperfect public monitoring. Our martingale approach

allows us to work out a clear connection between the discrete time and continuous

time payoff processes. A general proof of convergence is the open issue in this literature,

and I strongly belief that the characterization result reported here is the key to

solve this problem.