  We study singular value potentials of H\"older continuous
$GL_2(\mathbb{R})$-cocycles over hyperbolic systems whose canonical holonomies
converge and are H\"older continuous. Such cocycles include locally constant
$GL_2(\mathbb{R})$-cocycles as well as fiber-bunched
$GL_2(\mathbb{R})$-cocycles. We show that singular value potentials of
irreducible such cocycles have unique equilibrium states. Among the reducible
cocycles, we provide a characterization for cocycles whose singular value
potentials have more than one equilibrium states.
