For over 25 years, common belief has been widely viewed as necessary for joint behavior. But this is not quite correct. We show by example that what can naturally be thought of as joint behavior can occur without common belief. We then present two variants of common belief that can lead to joint behavior, even without standard common belief ever being achieved, and show that one of them, action-stamped common belief, is in a sense necessary and sufficient for joint behavior. These observations are significant because, as is well known, common belief is quite difficult to achieve in practice, whereas these variants are more easily achievable.

翻译：近25年来，共同信念一直被广泛视为联合行为产生的必要条件，但这一观点并不完全正确。我们通过实例表明，在缺乏共同信念的情况下，自然可被视为联合行为的现象仍有可能发生。继而提出两种共同信念的变体形式——即便从未达成标准的共同信念，它们也能促成联合行为，并证明其中一种变体（行为印记共同信念）在特定意义上构成联合行为的充要条件。这些发现具有重要意义，因为众所周知共同信念在实际中极难达成，而这类变体形式则更易实现。