S Equilibrium: A Synthesis of (Behavioral) Game Theory
arXiv:2307.06309
Abstract
equilibrium synthesizes a century of game-theoretic modeling. -beliefs determine choices as in the refinement literature and level-, without anchoring on Nash equilibrium or imposing ad hoc belief formation. -choices allow for mistakes as in QRE, without imposing rational expectations. equilibrium is explicitly set-valued to avoid the common practice of selecting the best prediction from an implicitly defined set of unknown, and unaccounted for, size. -equilibrium sets vary with a complexity parameter, offering a trade-off between accuracy and precision unlike in equilibrium. Simple "areametrics" determine the model's parameter and show that choice sets with a relative size of 5 percent capture 58 percent percent of the data. Goodness-of-fit tests applied to data from a broad array of experimental games confirm equilibrium's ability to predict behavior in and out of sample. In contrast, choice (belief) predictions of level- and QRE are rejected in most (all) games.