L.P.-games with sufficiently many players

L.P.-games aren-person cooperative games arising from a linear program as studied by Owen and Billera/Raanan. Employing a version of nondegeneracy of games developed by Weidner and the author, we show that methods from the Geometry of Numbers are the suitable tool in order to obtain lower bounds for the number of players of each type that ensure that the core and the competitive equilibrium coincide.