<p>This paper develops a competitive model of annuity and life insurance markets with private information about survival probabilities and public annuitization through Social Security. Households value retirement consumption and bequests, can save through a risk-free technology, and trade nonexclusive insurance contracts, so insurers cannot condition on households’ full portfolios. The paper has three main contributions. First, it establishes existence of competitive equilibrium in this environment. Second, it characterizes equilibrium market structure: at most one private mortality-contingent market is active, and greater public annuitization shifts the economy from annuities toward life insurance. Third, it derives the ex ante efficient allocation and the tax-transfer policy that implements it. A numerical illustration shows how higher Social Security benefits shrink annuity participation, worsen selection in the annuity pool, and raise annuity prices before private life insurance becomes the active market. The analysis links adverse selection, nonexclusive contracting, and public insurance to the endogenous structure of private insurance markets.</p>