On Milnor's classes ''L'' and ''D'' (Q1083383)

A twenty-one player counterexample is presented which disposes of two questions raised by \textit{J. W. Milnor} [''Reasonable outcomes for n-person games'', RM-916, Rand Corporation, Santa Monica (1952)] concerning the existence of certain pre-solutions, based on plausible lower and upper bounds to what a coalition should expect to receive in a cooperative game in characteristic function form. In the counterexample, the lower-bound set, known as ''L'', is empty, and the upper-bound set, known as ''D'', contains no efficient outcomes.