Supplement to “ Magical Thinking : A Representation Result ” ( For Online Publication )

This supplement contains extended formal results for Daley and Sadowski (2016) (henceforth DS16). Specifically, §S.1 establishes that in Prisoners’ Dilemma (PD) games, the model of DS16 is logically distinct from three models that employ well-known forms of other-regarding preferences: altruism (Ledyard, 1995; Levine, 1998), inequity aversion (Fehr and Schmidt, 1999), and reciprocity (Rabin, 1993). §S.2 provides an axiomatic characterization of F—the perceived distribution of types in the model—being empirically valid when there are infinitely many players. §S.3 extends the axiomatic analysis to symmetric 2⇥2 games beyond PD games. All references to numbered sections/axioms/results/etc. are from DS16, unless otherwise indicated.