 How can the non-psychological game theorist understand the concept of an NE that is an equilibrium in both actions and beliefs? Decades of experimental study have shown that when human subjects play games, especially games that ideally call for use of Bayes’s rule in making conjectures about other players’ beliefs, we should expect significant heterogeneity in strategic responses. Multiple kinds of informational channels typically link different agents with the incentive structures in their environments. Some agents may actually compute equilibria, with more or less error. Others may settle within error ranges that stochastically drift around equilibrium values through more or less myopic conditioned learning. Still others may select response patterns by copying the behavior of other agents, or by following rules of thumb that are embedded in cultural and institutional structures and represent historical collective learning. Note that the issue here is specific to game theory, rather than merely being a reiteration of a more general point, which would apply to any behavioral science, that people behave noisily from the perspective of ideal theory. In a given game, whether it would be rational for even a trained, self-aware, computationally well resourced agent to play NE would depend on the frequency with which he or she expected others to do likewise. If she expects some other players to stray from NE play, this may give her a reason to stray herself. Instead of predicting that human players will reveal strict NE strategies, the experienced experimenter or modeler anticipates that there will be a relationship between their play and the expected costs of departures from NE. Consequently, maximum likelihood estimation of observed actions typically identifies a QRE as providing a better fit than any NE. 