This chapter reviews recent experimental data testing game theory and behavioral models that have been inspired to explain those data. The models fall into four groups: in cognitive hierarchy or level-k models, the assumption of equilibrium is relaxed by assuming agents have beliefs about other agents who do less reasoning (i.e., some are non-strategic, and others are more strategic and understand they are playing non-strategic players). A different approach, quantal response equilibrium, retains equilibrium expectations but adds stochastic response (of which players are aware). Learning theories explain choices in games played repeatedly as a result of past actions and payoffs that were received (as in classical reinforcement) or foregone payoffs (model-directed learning). Finally, many studies reject the joint hypothesis of equilibrium expectations and optimization, along with self-interest in valuing outcomes. Social preference models have emerged to explain these data, capturing concepts like inequity-aversion, reciprocity, and social image.
