This paper studies the retirement incentives induced by the U.S. Social Security system in a framework which allows for different degrees of cooperation and strategic interaction between spouses. We develop a model in which spouses maximize a joint household utility function, subject to the additional constraint that---conditional on the partner's optimal response--- neither one finds it optimal to deviate from the best constrained household allocation by either changing labor force status or by claiming disability or early retirement benefits. We show that accounting for "non-cooperative" behavior through this additional constraint can rationalize various choices of older US couples observed in the 1932-42 cohort of the Health and Retirement Study. In particular non-cooperative behavior helps in the explanation of two recurring puzzles in the retirement literature: (i) the clustering of benefit claiming at the early age of 62; (ii) the joint benefit claiming of couples. We contrast our findings to those from a standard model, extended to include a process for declining health and complementarities in retirement leisure between spouses, and show that the latter can rationalize neither early nor joint claiming behavior whenever individuals can make benefit claiming decisions and labor force participation decisions separately. Finally, we assess the importance of variable health costs and of bequest motives in determining retirement-age decisions. Our non-cooperative model offers interesting insights on welfare and policy.