  McLennan and Tourky (2010) showed that "imitation games" provide a new view
of the computation of Nash equilibria of bimatrix games with the Lemke-Howson
algorithm. In an imitation game, the payoff matrix of one of the players is the
identity matrix. We study the more general "unit vector games", which are
already known, where the payoff matrix of one player is composed of unit
vectors. Our main application is a simplification of the construction by Savani
and von Stengel (2006) of bimatrix games where two basic equilibrium-finding
algorithms take exponentially many steps: the Lemke-Howson algorithm, and
support enumeration.
