Managed health care plans and providers in the US and elsewhere sell their services to multiple payers. For example, the three largest groups of purchasers from health plans in the US are employers, Medicaid plans, and Medicare, with the first two accounting for over 90% of the total enrollees. In the case of hospitals, Medicare is the largest buyer, but it alone only accounts for 40% of the total payments. While payers have different objectives and use different contracting practices, the plans and providers set some elements of the quality in common for all payers. In this paper, we study the interactions between a public payer, modeled on Medicare, which sets a price and takes any willing provider, a private payer, which limits providers and pays a price on the basis of quality, and a provider/plan, in the presence of shared elements of quality. The provider compromises in response to divergent incentives from payers. The private sector dilutes Medicare payment initiatives, and may, under some circumstances, repair Medicare payment policy mistakes. If Medicare behaves strategically in the presence of private payers, it can free-ride on the private payer and set its prices too low. Our paper has many testable implications, including a new hypothesis for why Medicare has failed to gain acceptance of health plans in the US.