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We examine vertical integration and exclusive behavior in health care markets in which insurers and hospitals bilaterally bargain over contracts. We employ a bargaining model of two hospitals and two health insurers competing on premiums. We show that asymmetric equilibria exist in which one insurer contracts one hospital whereas the other insurer contracts both hospitals, even if all players are equally efficient in their production. Asymmetric equilibria arise if hospitals are sufficiently differentiated. In these cases, total industry profits increase and consumer welfare decreases in comparison to the case in which both insurers have contracts with both hospitals. Vertical integration makes these equilibria possible for a wider range of parameters.