  The rank of a bimatrix game is defined as the rank of the sum of the payoff
matrices of the two players. The rank of a game is known to impact both the
most suitable computation methods for determining a solution and the expressive
power of the game. Under certain conditions on the payoff matrices, we devise a
method that reduces the rank of the game without changing the equilibrium of
the game. We leverage matrix pencil theory and the Wedderburn rank reduction
formula to arrive at our results. We also present a constructive proof of the
fact that in a generic square game, the rank of the game can be reduced by 1,
and in generic rectangular game, the rank of the game can be reduced by 2 under
certain assumptions.
