Representation and Bracketing in Repeated Games

In this experimental paper, the author investigates the framing effect of different representations of multiple strategic settings or games on a player’s strategic behavior. Two representations of the same environment are employed, wherein a player engages in two infinitely repeated prisoner’s dilemma games. In the first representation (termed Split), the stage games are shown separately. In contrast, the second representation (termed Linked) displays a combined stage game. The choice bracketing, distinguishing between Narrow and Broad bracketing, is considered a potential cause behind any disparity in behavior between the two representations. The Split representation does not necessitate broad bracketing, whereas the Linked representation compels it. Each type of bracketing has its own equilibrium implications. The author employs both a between-subject design (Study 1), where each subject observes only one representation, and a within-subject design (Study 2), where each subject is shown both the Linked and Split representations. In Study 1, significant differences in average behavior between the two representations are observed for both symmetric and asymmetric payoffs, albeit only after conditioning for session fixed effects. Study 2 reveals a more prominent effect of representation, and a sequence effect is observed, wherein the tendency to defect in both games is higher in the Linked representation if administered after the Split representation. In Study 2, for individuals who cannot be categorized as broad bracketers, the effect of seeing the Linked representation instead of the Split representation is economically significant. It increases the probability of choosing to cooperate in both games by more than 20% and decreases the probability to defect in both games by more than 25%.