In this note a partial solution of Open Problem 41C of Aumann and Shapley (1974) is presented. A sufficient condition for the Aumann-Shapley value of a market game to exist, to be contained in its core, and to be the competitive payoff distribution of a transferable utility competitive...

The concept of a value of a coalitional game, in the spirit of R.J. Aumann and L.S. Shapley, is extended to the case of games with fuzzy coalitions, providing new and heuristically meaningful insights into the game theoretical context, which have some significant impact on balance and equilibria...