In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. We also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regula...

Rational secret sharing is a fundamental primitive at the intersection of cryptography and game theory. In essence, a dealer wishes to engineer a communication game that, when rationally played, guarantees that each of the players learns the dealer’s secret. Yet, all solutions so far were quite inefficient and relied on the players’ beliefs and not just on their rationality. After providing a m...