We reduce the number of open additivity problems in quantum information theory by showing that four of them are equivalent. Namely, we show that the conjectures of additivity of the minimum output entropy of a quantum channel, additivity of the Holevo expression for the classical capacity of a quantum channel, additivity of the entanglement of formation, and strong superadditivity of the entang...

We give an axiomatization of the aspiration core on the domain of all TU-games using a relaxed feasibility condition, non-emptiness, individual rationality, and generalized versions of the reduced game property (consistency) and superadditivity. Our axioms also characterize the C-core ([Guesnerie and Oddou, 1979] and [Sun, Trockel, and Yang, 2008]) and the core on appropriate subdomains. The la...

A natural extension of superadditivity is not sufficient to imply that the grand coalition is efficient when externalities are present. We provide a condition, analogous to convexity, that is sufficient for the grand coalition to be efficient and show that this also implies that the (appropriately defined) core is nonempty. Moreover, we propose a mechanism which implements the most efficient pa...

Why are human inferences sometimes remarkably close to the Bayesian ideal and other times systematically biased? In particular, why do humans make near-rational inferences in some natural domains where the candidate hypotheses are explicitly available, whereas tasks in similar domains requiring the self-generation of hypotheses produce systematic deviations from rational inference. We propose t...