  Statistical mechanics is based on interplay between energy minimization and
entropy maximization. Here we formalize this interplay via axioms of
cooperative game theory (Nash bargaining) and apply it out of equilibrium.
These axioms capture basic notions related to joint maximization of entropy and
minus energy, formally represented by utilities of two different players. We
predict thermalization of a non-equilibrium statistical system employing the
axiom of affine covariance|related to the freedom of changing initial points
and dimensions for entropy and energy|together with the contraction invariance
of the entropy-energy diagram. Whenever the initial non-equilibrium state is
active, this mechanism allows thermalization to negative temperatures.
Demanding a symmetry between players fixes the final state to a specific
positive-temperature (equilibrium) state. The approach solves an important open
problem in the maximum entropy inference principle, {\it viz.} generalizes it
to the case when the constraint is not known precisely.
