Misspecification, equilibrium and rational choice

We consider learning in settings that are misspecified in that a decision maker is unable to learn the true probability distribution over outcomes. Under misspecification, Bayes' rule might not converge to the model that leads to actions with the highest objective payoff among the models subjectively admitted by the decision maker. Higher objective payoffs can be obtained by learning rules that learn directly from payoffs. Less obviously, when we consider an objective function that combines (i) payoff optimization with (ii) a desire to be closer to the truth, the standard Bayesian paradigm can lead to outcomes that are Pareto inefficient. This arises from the fact that the standard paradigm, in effect, finds a Nash equilibrium of a game played by two fictional players (one who chooses beliefs given actions, another who chooses actions given beliefs). As this equilibrium need not be in the core, it may that the outcome is inefficient.

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A link to a short working paper of what Jonathan presented: https://papers.ssrn.com/abstract=4005854