= Complementarity construction of a symmetric Nash equilibrium
{title2=$Px+z=\mathbf1,\quad x,z\geq0,\quad x^{\mathsf T}z=0$}
For a symmetric <bimatrix game> with payoff matrices $P,P^{\mathsf T}$, any nonzero $x$ satisfying these equations gives the symmetric <Nash equilibrium> $(x/\sum_i x_i,x/\sum_i x_i)$. Every positive coordinate attains the same maximal payoff. This one-vector construction differs from a two-vector <Lemke-Howson algorithm> path, which can return asymmetric equilibria.
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