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  and Mailath, Matthews and Sekiguchi  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. Our result provides a general explanation for the findings of Kandori and Obara  and Mailath, Matthews and Sekiguchi  as well as a general method for constructing examples of that sort.
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