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Equilibrium in a Bargaining Game of Two Sellers and Two Buyers

Author

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  • Jiawei Li

    (School of Computer Science, University of Nottingham Ningbo China, Ningbo 315100, China)

  • Tianxiang Cui

    (School of Computer Science, University of Nottingham Ningbo China, Ningbo 315100, China)

  • Graham Kendall

    (School of Computer Science, University of Nottingham UK, Nottingham NG7 2RD, UK)

Abstract

The uniqueness of equilibrium in bargaining games with three or more players is a problem preventing bargaining theory from general real world applications. We study the uniqueness of bargaining equilibrium in a bargaining game of two sellers and two buyers, which has instances in real-world markets. Each seller (or buyer) wants to reach an agreement with a buyer (or seller) on the division of a pie in the bargaining game. A seller and a buyer will receive their agreed divisions if they can reach an agreement. Otherwise, they receive nothing. The bargaining game includes a finite number of rounds. In each round, a player can propose an offer or accept an offer. Each player has a constant discounting factor. Under the assumption of complete information, we prove that the equilibrium of this bargaining game is the same division of two pies. The ratio of division as a function of the discount factors of all players is also deduced. The result can be extended to a bargaining game of n -sellers and n -buyers, which reveals the relevance of bargaining equilibrium to the general equilibrium of a market.

Suggested Citation

  • Jiawei Li & Tianxiang Cui & Graham Kendall, 2022. "Equilibrium in a Bargaining Game of Two Sellers and Two Buyers," Mathematics, MDPI, vol. 10(15), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2705-:d:876615
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    References listed on IDEAS

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