Before revision: This paper proposes a foundation for heterogeneous beliefs in games, in which disagreement arises not because players observe different information, but because they learn from common information in different ways. Players may be misspecified, and may moreover be misspecified about how others learn. The key assumption is that players nevertheless have some common understanding of how to interpret the data; formally, players have common certainty in the predictions of a class of learning rules.
After revision: Players are statistical learners who learn about payoffs from data. They may interpret the same data differently, but have common knowledge of a class of learning rules.