Many developed countries rely, to varying degrees, on competition among private health plans to obtain affordable and high-quality health insurance for their residents. Incorporating beneficiary-level competitive bidding into these healthcare systems can better align the incentives of these health plans, increase their willingness to enroll, and serve the sickest and most vulnerable patients while keeping costs manageable. We identify two digitally enabled program designs that allow private insurance plans to competitively bid to enroll individual beneficiaries. Compared with those used in existing entitlement programs, these designs always make a larger share of the beneficiary population profitable to enroll, thereby increasing willingness of the plans to enroll the most costly beneficiaries and improving access to care. On simulating the conditions of existing real-word healthcare entitlement programs, we found that these new designs actually tend to lower the tax burden in up to 83% of simulations. The research findings suggest that these new designs hold great promise in achieving the dual aim of improved access and lower costs. We believe that findings from this research can guide policymakers implement policies that will enroll more beneficiaries and cost the taxpayers less.