This paper first establishes a new core theorem using the concept of generated payoffs: the TU (transferable utility) core is empty if and only if the maximum of generated payoffs (mgp) is greater than the grand coalition’s payoff v(N), or if and only if it is irrational to split v(N). It then...

This note provides two necessary and sufficient conditions for the relative interior of the core (and the base polyhedron) to be non-empty: (i) the second largest excess of the prenucleolus is negative; (ii) the grand coalition's payoff is greater than the minimum no-blocking payoff. Such...

This paper provides a TU < alpha >-core existence result in a large class of normal form games. In the oligopoly markets of a homogeneous good, the TU < alpha >-core is non-empty if all profit functions are continuous and concave. In a general game, the existence of TU < alpha >-core follows from the weak separability,...</alpha></alpha></alpha>