Before revision: We introduce a set-valued generalization of Nash equilibrium, called M equilibrium, which is based on ordinal monotonicity - players' choice probabilities are ranked the same as the expected payoffs based on their beliefs - and ordinal consistency - players' beliefs yield the same ranking of expected payoffs as their choices. Using results from semi-algebraic geometry, we prove there exist a finite number of M equilibria, each consisting of a finite number of connected components. Generically, M-equilibria can be "color coded" by their ranks in the sense that choices and beliefs belonging to the same M equilibrium have the same color. We show that colorable M equilibria are behaviorally stable, a concept that strengthens strategic stability. Furthermore, set-valued and parameter-free M equilibrium envelopes various parametric models based on fixed-points, including QRE as well as a new andcomputationally simpler class of models called \mu Equilibrium .
After revision: We introduce a set-valued generalization of Nash equilibrium, called M equilibrium, to capture empirical regularities from over half a century of game-theory experiments. We show M equilibrium serves as a meta theory for various models that hitherto were considered unrelated. M equilibrium is empirically robust and, despite being set-valued and parameter-free M equilibrium envelopes various parametric models based on fixed-points, including QRE as well as a new andcomputationally simpler class of models called \mu Equilibrium .