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>

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...