Motivated by recent empirical work, this paper formalizes a theory of competitive savings - an arms race in household savings for mating competition that is made more fierce by an increase in the male-to-female ratio in the pre-marital cohort. Relative to the empirical work, the theory can clarify a number of important questions: What determines the strength of the savings response by males (or households with a son)? Can women (or households with a daughter) dis-save? What are the conditions under which aggregate savings would go up in response to a higher sex ratio? This theory can potentially help to understand the savings patterns in China, India, Vietnam, Singapore, Hong Kong, and other economies that have experienced a dramatic increase in the pre-marital sex ratio.