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. The common prior assumption is nested as the special case in which this class is a singleton . The main results characterize which rationalizable actions and Nash equilibria can be predicted when agents observe a finite quantity of data , and how much data is needed to predict various solutions. This number of observations needed depends on the degree of strictness of the solution and speed of common learning .
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 procedures. I propose a metric for the analyst's "confidence" in a strategic prediction, based on the probability that the prediction is consistent with the realized data . The main results characterize the analyst's confidence in a given prediction as the quantity of data grows large, and provide bounds for small datasets. The approach generates new predictions, e.g. that speculative trade is more likely given high-dimensional data, and that coordination is less likely given noisy data .
R
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
Players are statistical learners who learn about payoffs from data. They may interpret the same data differently, but have common knowledge
R
rules. The common prior assumption is nested as the special case in which this class is a singleton
procedures. I propose a metric for the analyst's "confidence" in a strategic prediction, based on the probability that the prediction is consistent with the realized data
R
which rationalizable actions and Nash equilibria can be predicted when agents observe a finite
the analyst's confidence in a given prediction as the
R
, and how much data is needed to predict various solutions. This number of observations needed depends on the degree of strictness of the solution and speed of common learning
grows large, and provide bounds for small datasets. The approach generates new predictions, e.g. that speculative trade is more likely given high-dimensional data, and that coordination is less likely given noisy data