Understanding Human Behavior via Similarity: A Geometric and Behavioral Rules-based Approach to Games

We study similarity in the complete set of one-shot 2×2 games with payoffs from {1, 2, 3, 4} without replacement. Similarity is defined geometrically via a neighborhood structure on games and continuity of behavior, and is applied to both theoretical rules (e.g., Nash equilibrium, level-k reasoning) and experimental data. This produces a partition of the games into (theoretical or empirical) similarity classes. We run a large-scale experiment in which each subject plays all 78 games within our class without feedback. We find that empirically inferred similarity classes diverge sharply from those predicted by Nash equilibrium and dominance reasoning. Instead, the empirical similarity classes align closely with the theoretical classes of a level-k variant, with deviations reflecting fairness and efficiency concerns. At the individual level, subjects' play can be classified according to primary and secondary rules, conforming with either level-k variant (0 ≤ k ≤ 5) or a fairness and efficiency-based heuristic. The main insights extend to strategic settings beyond our 2 × 2 games.