The bilateral consistent prekernel for (boundary) balanced games and ordinal prekernels for economic environments

It is proved that the bilateral consistent prekernel is not empty and intersects the core of (boundary) balanced games. The proof is introduced in a general framework, which enables us to apply it to pure exchange economy environments. As a result a family of non-empty ordinal solution concepts that intersect the core is defined directly on the economy environment. Such solution concepts that are defined by means of individual excesses associated with the economy may be considered as ordinal (pre) kernels. While a canonical ordinal (pre) kernel does not arise naturally, a parallel approach to that used to derive an ordinal Shapley value yields one of them.