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We introduce a set-valued solution concept, 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, falsifiable. Results from a series of experiments that compare M equilibrium to leading behavioral game theory models demonstrate its virtues in predicting observed choices and stated beliefs. Data from experimental games with a unique pure-strategy Nash equilibrium and multiple M equilibria exhibit coordination problems that could not be anticipated through the lens of existing models.