= Equilibrium oddness theorem
A finite nondegenerate <bimatrix game> has a finite odd number of <Nash equilibria>. After shifting to positive payoffs, fully labelled vertex pairs in the bounded best-response polytopes correspond to equilibria plus one artificial zero pair. Dropping a fixed label gives a finite path graph whose endpoints are exactly these pairs. The number of endpoints is even, leaving an odd number of genuine equilibria. This is the endpoint-parity argument underlying the <Lemke-Howson algorithm>.
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