Impartial loopy games are susceptible to analysis by the generalized Sprague-Grundy theorem.
A loopy game is a pair G = (V, x), where V is a bipartite graph with named edge-sets (that is, some edges of the bipartite graph are Left, and other edges are Right) and x is the start vertex (initial position) of a game.
This labeled bipartite graph is called a bigraph in combinatorial game theory.
Stoppers are loopy games that have no subpositions with infinite alternating runs.
Unlike generic loopy games, stoppers can never tie.