Co-action equilibrium fails to predict choices in mixed-strategy settings

Abstract

Social projection is the tendency to project one's own characteristics onto others. This phenomenon can potentially explain cooperation in prisoner's dilemma experiments and other social dilemmas. The social projection hypothesis has recently been formalized for symmetric games as co-action equilibrium and for general games as consistent evidential equilibrium. These concepts have been proposed to predict choice behavior in experimental one-shot games. We test the predictions of the co-action equilibrium concept in a simple binary minimizer game experiment. We find no evidence of social projection.In social psychology, social projection is the well-established tendency of people to project their own preferences, beliefs and behaviors onto other members of their own social groups 1 . This concept grew out of early research on the false consensus effect 2 and has been extensively studied in recent decades 3 . In decision-making contexts, social projection results from evidential reasoning 4 . According to the theory of evidential decision-making, this kind of reasoning is evoked when an agent perceives other agents about whom he has no specific knowledge as belonging to the same social group as he does (his ingroup) and as being in the same decision-making situation. The agent then treats his own decision as diagnostic for the other agents' decisions; i.e., he projects his own choices onto them. When transferred to a strategic context, this means that a player in a symmetric game believes that other players will choose the same (possibly mixed) strategy as she herself does.Evidential reasoning is relatively uncontroversial if applied after one's own choice has been made. However, some researchers have proposed evidential reasoning as a rational way to choose a strategy by deliberating on the consequences of one's own hypothetical choices in combination with the resulting choices of others. According to this view, a player in a prisoner's dilemma situation should reason that if she cooperates, her opponent will be likely to cooperate as well, whereas if she defects, he will also be likely to defect. Comparing her own payoffs in the two resulting strategy profiles, (C, C) and (D, D), will then lead the player to choose cooperation. Early arguments along these lines have been prominently-and controversially-presented by Rapoport 5 and Hofstadter 6