This article extends Simpson's (2003) research on sex differences in social dilemmas. To test the hypotheses that men defect in response to greed and women to fear, Simpson created Fear and Greed Dilemmas, but experiments using these games supported the greed hypothesis only. In this article I focus on why the fear hypothesis failed and suggest that fear was actually absent in the Fear Dilemma. To retest Simpson's hypotheses, I propose a new asymmetric game, the Fear-of-Greed Dilemma. The asymmetry is important for two reasons. First, it creates the risk of exploitation that Simpson's Fear Dilemma lacked. Second, it exposes a critical limitation in Rapoport's (1964) K-index and suggests a re-specification. Laboratory studies supported the fear hypothesis and found mediating effects of expectations about partners on sex differences in cooperation.