  We address the problem of existence and (non-)uniqueness of solutions
$\big(c,u(\cdot),\mu\big)$ to ergodic mean-field games in the whole space
$\mathbb{R}^{m}$ with unbounded and merely measurable data, and for
non-separable Hamiltonian. The payoff functional satisfies a new monotonicity
condition, different from the usual one due to Lasry and Lions. The method we
use is also different from classical approaches. It relies on duality theory
and optimization in abstract Banach spaces together with maximal dissipativity
of diffusion operators.
