S Equilibrium: A Synthesis of (Behavioral) Game Theory

TL;DR

S equilibrium offers a comprehensive framework combining behavioral game theory elements, allowing for flexible, explicit set-valued predictions that better fit experimental data than traditional models like level-k or QRE.

Contribution

It introduces S equilibrium, a novel set-valued solution concept synthesizing various behavioral game theory models without relying on Nash equilibrium assumptions.

Findings

Choice sets with 5% size capture 58% of data

S equilibrium outperforms level-k and QRE in predictive accuracy

Model's parameter determined by simple areametrics

Abstract

$S$ equilibrium synthesizes a century of game-theoretic modeling. $S$-beliefs determine choices as in the refinement literature and level-$k$, without anchoring on Nash equilibrium or imposing ad hoc belief formation. $S$-choices allow for mistakes as in QRE, without imposing rational expectations. $S$ 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. $S$-equilibrium sets vary with a complexity parameter, offering a trade-off between accuracy and precision unlike in $M$ 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 $S$ equilibrium's ability to predict behavior in and out of sample. In contrast, choice (belief) predictions of level-$k$ and QRE are rejected in most (all) games.