In this paper, an alternative definition of stable sets, defined by mertens [mertens, 1989. Stable equilibria – a reformulation. Part i. Definitions and basic properties. Mathematics of operations research 14, 575–625], is given where perturbations are interpreted as restrictions on the strategy space instead of perturbations of the payoffs. This alternative interpretation is then used to compute a special type of stable sets –called standard stable sets – in the context of bimatrix games, exclusively using linear optimization techniques and finite enumerations.