We establish that in the Prisoners' Dilemma, the model of Daley and Sadowski (2014) 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,...

We provide axiomatic foundations for a simple model of play in prisoners' dilemma games. The model accommodates cooperation and suggests that players behave as if their expectations about their opponents' behavior vary with their own choice. We refer to this nonstandard updating as magical...