Recent healthcare reforms have sought to increase efficiency by introducing managed care (MC) while respecting consumer preferences by admitting choice between MC and conventional care. This article proposes an institutional change designed to let German consumers choose between the two settings through directing payments from the Federal Health Fund to social health insurers (SHIs) or to specialized MC organizations (MCOs). To gauge the chance of success of this reform, a game involving a SHI, a MCO, and a representative insured (RI) is analyzed. In a “three-player/three-cake” game the coalitions {SHI, MCO}, {MCO, RI}, and {SHI, RI} can form. Players’ possibility to switch between coalitions creates new outside options, causing the conventional bilateral Nash bargaining solution to be replaced by the so-called von Neumann-Morgenstern triple. These triples are compared to the status quo (where the RI has no threat potential) and related to institutional conditions characterizing Germany, the Netherlands, and Switzerland.