In many applications of computer vision and pattern recognition which use graph-based knowledge representation, it is of great interest to be able to extract the K largest cliques in a graph, but most methods are geared either towards extracting the single clique of maximum size, or enumerating all cliques, without following any particular order. In this paper we present a novel approach for partial clique enumeration, that is, the extraction of the K largest cliques of a graph. Our approach is based on a continuous formulation of the clique problem developed by Motzkin and Straus, and is able to avoid extracting the same clique multiple times. This is done by casting the problem into a game-theoretic framework and iteratively rendering unstable the solutions that have already been extracted.