In general, consideration of the non-cooperative case of a two-person non-zero-sum game leads to a more restricted set of feasible outcomes than the cooperative oase of the same game since correlated strategies are not permitted# An approach to describing such set of feasible outcomes for a class of games is given. Characterization seems plausible but there still are some open questions. The class of games of interest is one defined by a 2 by 2 bimatrix game having two pure strategy non-permutable equilibrium points, one for each player, and a third equilibrium point with the same features as the others given by the threat strategies.