Symmetric bimatrix game
= Symmetric bimatrix game
{title2=$Q=P^T$}
A square <bimatrix game> is symmetric when exchanging players exchanges their payoffs: its <payoff matrices> are $P,Q$ with $Q=P^T$. If $(x,y)$ is a <Nash equilibrium>, then $(y,x)$ is also a <Nash equilibrium>. A <symmetric bimatrix game> can still have asymmetric equilibria, so the two strategy vectors must be kept separate in the <Lemke-Howson algorithm>.