We analyze a two-sided search model in which we assume utility is not perfectly transferable. Except for this assumption the model is standard, yet it generates results that are quite different from those obtained in models with transferable utility. In particular, the model has multiple equilibria, even with constant returns to scale in the meeting technology. We also provide conditions to guarantee uniqueness in equilibrium search models with or without transferable utility. These conditions apply even with increasing returns in the meeting technology. Examples and applications are discussed. (Copyright: Elsevier)
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