This note considers a bargaining environment with two-sided asymmetric information and quasilinear preferences in which parties select bargaining mechanism after learning their valuations. I demonstrate that sometimes the buyer achieves a higher ex-ante payoff if the bargaining mechanism is selected by her opponent rather than by herself. In the model, the buyer has limited wealth and in addition to acquiring one good from the seller can purchase a different good from a competitive market. The positive relation between the values of these goods is what delivers our result.
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