We develop a new paradigm to study social dilemmas, called exchange dilemmas. Exchange dilemmas arise from externalities of exchanges with third parties, and many real-life social dilemmas are more accurately modeled as exchange dilemmas rather than prisoner's dilemmas. Building on focusing and framing research we predict that defection is omnipresent in exchange dilemmas, which is corroborated in to very different experiments. Our results suggest that the fundamental problem of cooperation in many real-life social dilemmas may be more severe and harder to solve than suggested by traditional prisoner's dilemma research, due to the presence of third parties. Directions for future research are suggested, focusing on relations with third parties.