  We introduce a two-player game involving two tokens located at points of a
fixed set. The players take turns to move a token to an unoccupied point in
such a way that the distance between the two tokens is decreased. Optimal
strategies for this game and its variants are intimately tied to Gale-Shapley
stable marriage. We focus particularly on the case of random infinite sets,
where we use invariance, ergodicity, mass transport, and deletion-tolerance to
determine game outcomes.
