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. ∗The authors thank Jeff Ely, Johannes Hörner, Michihiro Kandori, George Mailath, Ichiro Obara, and Ofer Zeitouni for helpful conversations. Financial assistance from National Science Foundation Grant # 0721090 is gratefully acknowledged. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.