We introduce ideas and methods from distribution theory into value theory. This novel approach enables us to construct new diagonal formulas for the Mertens value and the Neyman value on a large space of non-differentiable games. This in turn enables us to give an affirmative answer to the...

We prove that every continuous value on a space of vector measure market games $Q$, containing the space of nonatomic measures $NA$, has the \textit{conic property}, i.e., if a game $v\in Q$ coincides with a nonatomic measure $\nu$ on a conical diagonal neighborhood then $\varphi(v)=\nu$. We...

We prove that a single-valued solution of perfectly competitive TU economies underling nonatomic exact market games is uniquely determined as the Mertens value by four plausible value-related axioms. Since the Mertens value is always a core element, this result provides an axiomatization of the...

We prove that a single-valued solution of perfectly competitive TU economies underling nonatomic vector measure market games is uniquely determined as the Mertens (1988) value by four plausible value-related axioms. Since the Mertens value is always in the core of an economy, this result...

Among the single-valued solution concepts studied in cooperative game theory and economics, those which are also positive projections play an important role. The value, semivalues, and quasivalues of a cooperative game are several examples of solution concepts which are positive projections....