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Interdependent Bargains

Author

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  • Zhou, Yihang
  • Sibley, David

Abstract

A seller bargains with two buyers to make a deal with each of them, using an alternating-offer protocol (“AO”). The bargaining begins with one buyer, with the second entering at a future date. The seller has a concave utility function, defined over total payments made by the two buyers. Hence, the bargain made with one buyer affects the outcome of the bargain made with the second buyer. The curvature properties of the seller utility and the arrival date of the second buyer decide how bargains affect each other. We derive dynamic properties of the negotiated prices. These prices exhibit unusual comparative statics. The price paid by the first buyer can be non-monotone in the discount factor used in the AO bargaining. This is because the bargaining between the seller and the first buyer anticipates the arrival of the second buyer. We extend the model to include downstream competition between the two buyers. We obtain results on first-mover and second-mover advantage.

Suggested Citation

  • Zhou, Yihang & Sibley, David, 2026. "Interdependent Bargains," Journal of Mathematical Economics, Elsevier, vol. 122(C).
    • Handle: RePEc:eee:mateco:v:122:y:2026:i:c:s0304406826000017
    DOI: 10.1016/j.jmateco.2026.103213
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