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A specific bargaining game is studied, motivated by the speech-making, billproposing, and bill-vetoing observed in legislative processes. The game has two players, a chooser and a proposer, with the preferences of the chooser not known to the proposer. The chooser starts the game by talking. Then the proposer proposes an outcome, which the chooser accepts or vetoes. Only two kinds of perfect equilibria exist. In the more interesting kind the chooser tells the proposer which of two sets contains his type. Two proposals are possibly elicited, a compromise proposal and the proposer's favorite proposal. Ironically, only the compromise proposal is ever vetoed.
Steven A. Matthews (Mon,) studied this question.