Complementary pivoting
= Complementary pivoting
{title2=$x_ir_i=0,\quad y_js_j=0$}
Complementary pivoting follows adjacent bases while maintaining all but one label of a complementarity system. The <Lemke-Howson algorithm> for a <bimatrix game> follows the duplicated label between two tableaux until it restores the dropped label at a nonzero completely labelled pair. Normalization then gives a <Nash equilibrium>.