12.4.6 Discussion Condition AI

In Theorem 12.4, we assume that a player's hierarchy is consistent with a common prior μ which satisfies Condition AI. This is an elicitable assumption because it is about beliefs, but it is arguably somewhat opaque. As noted earlier, we conjecture that common priors satisfying Condition AI may be characterized via a suitable no-betting condition. This would provide a more transparent behavioral characterization.

We emphasize that we cannot interpret Condition AI, i.e., [12.13], directly as a restriction on Player i's beliefs: in our environment, players do not have beliefs about their own strategies. Instead, it is a restriction on the beliefs of the other players, and perhaps those of an outside ...

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