Two key features distinguish the general class of recursive preferences from the standard model of dynamic choice: (i) agents may care about the intertemporal distribution of risk, and (ii) their rates of time preference, rather than being fixed, may vary with the level of consumption. We investigate what these features imply in the context of a repeated strategic interaction. First, we show that opportunities for intertemporal trade may expand the set of feasible payoffs relative to that in a static interaction. Two distinct sources for such trade are identified: endogenous heterogeneity in the players' rates of time preference and a hedging motive pertaining to the intertemporal distribution of risk. The set of equilibrium payoffs may on the other hand shrink drastically as many efficient outcomes become unsustainable no matter the level of patience. This “antifolk” result occurs when the players prefer stage outcomes to be positively correlated rather than independent across time. Intuitively, such preferences make it inefficient to offset short‐term losses with future gains, while this is needed to ensure that security levels are met on path. We also establish a folk theorem: if security levels are met on path, such play can be sustained in a subgame perfect equilibrium provided that the players are sufficiently patient.