Recall and private monitoring

For a general class of games with private monitoring we show for any finite state strategy (or automaton strategy) with Di states for players i∈{1,…,N}, if there exists a number of periods t such that it is possible on-path to reach any joint state from any joint state in t periods, the strategy is a strict correlated equilibrium only if each player's strategy is a function only of what the player observes in the last Di−1 periods.