From 1960 to 1969 he studied mathematics at the Hebrew University of Jerusalem (BSc, MSc, and PhD), the advanced degrees under the supervision of Robert Aumann.
He suggested a new approach to solving cooperative games – the nucleolus – based on equity as well as feasibility considerations.
Robert Aumann and Michael Maschler, in a paper published in 1985, showed that a conundrum from the Babylonian Talmud, which defied scholars’ attempts at comprehension over two millennia, was naturally resolved when applying the concept of the nucleolus.
Schmeidler was the first to propose a general-purpose, axiomatically-based decision theoretic model that deviated from the Bayesian dictum, according to which any uncertainty can and should be quantified by probabilities.
Rather, along the lines attributed to Frank Knight and John Maynard Keynes, the argument is normative, suggesting that it is not necessarily more rational to be Bayesian than not.