Title: Blackwell correlated equilibrium (joint with Doron Ravid).

Abstract: We develop a method for making robust predictions in games with flexible information acquisition (i.e., rational inattention, Sims 2003). In games with exogenous information, one can describe the set of attainable outcomes using the Bayes correlated equilibrium (BCE) concept (Bergemann and Morris 2016). We introduce a refinement of BCE, Blackwell correlated equilibrium (BKE), and prove that it spans all outcomes attainable under some flexible learning technology whose costs increase in Blackwell's (1951,1953) information order. We show the BKE set is either dense or nowhere dense in the BCE set, with the former being true for generic games. We also characterize the set of outcomes attainable under almost-free learning. We conclude by exploring the implications of BKE on a Bertrand competition game, where we show the best BCE for consumers may not be approximable by BKEs.