Equivalence of public mixed-strategies and private behavior strategies in games with public monitoring

In repeated games with public monitoring, the consideration of behavior strategies makes relevant the distinction between public and private strategies. Recently, Kandori and Obara [6] and Mailath, Matthews and Sekiguchi [8] have provided examples of games with equilibrium payoffs in private strategies which lie outside the set of Public Perfect Equilibrium payoffs. The present paper focuses on another distinction, that between mixed and behavior strategies. It is shown that, as far as with mixed strategies one is concerned, the restriction to public strategies is not a restriction at all.