Proto-coalition bargaining and the core

In the proto-coalition model of government formation, formateur F appoints a proto-coalition and asks its members whether to start negotiating a coalition contract. If all accept, then the proto-coalition forms and starts negotiating; otherwise a caretaker government assumes office. I extend this model by allowing F to revise the chosen proto-coalition after rejections, that he states pre-conditions for the subsequent negotiations, and that F's opponents may publicly pre-commit to accept/reject certain proposals. The set of equilibrium outcomes is identified as the core if F's opponents can pre-commit and as the convex hull of the core if they cannot pre-commit credibly. This extended model eliminates two flaws of the standard model: it explains why F cannot always install his favored coalition (whatever the status quo) and why "important" coalition members may have more bargaining power in the subsequent negotiations than others.