In this paper upper cycle free effectivity functions are implemented b
y strategic claim game correspondences. Conditions are provided such t
hat an effectivity function coincides with the alpha- and beta-effecti
vity functions corresponding to its associated claim game corresponden
ce. Furthermore, the notion of the core of an effectivity function is
extended to subsets of alternatives, and it is shown that for upper cy
cle free effectivity functions this so-called setcore is always non-em
pty. Moreover, given a preference profile, relations between the setco
re of an effectivity function and strong Nash equilibria of the associ
ated claim game correspondence are established. Journal of Economic Li
terature Classification Numbers: 025, 026. (C) 1995 Academic Press, In
c.