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Article

Equilibrium in a Bargaining Game of Two Sellers and Two Buyers

1
School of Computer Science, University of Nottingham Ningbo China, Ningbo 315100, China
2
School of Computer Science, University of Nottingham UK, Nottingham NG7 2RD, UK
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(15), 2705; https://doi.org/10.3390/math10152705
Submission received: 6 July 2022 / Revised: 27 July 2022 / Accepted: 28 July 2022 / Published: 30 July 2022
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)

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.
Keywords: bargaining; Nash bargaining equilibrium; bargaining game of two sellers and two buyers bargaining; Nash bargaining equilibrium; bargaining game of two sellers and two buyers

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MDPI and ACS Style

Li, J.; Cui, T.; Kendall, G. Equilibrium in a Bargaining Game of Two Sellers and Two Buyers. Mathematics 2022, 10, 2705. https://doi.org/10.3390/math10152705

AMA Style

Li J, Cui T, Kendall G. Equilibrium in a Bargaining Game of Two Sellers and Two Buyers. Mathematics. 2022; 10(15):2705. https://doi.org/10.3390/math10152705

Chicago/Turabian Style

Li, Jiawei, Tianxiang Cui, and Graham Kendall. 2022. "Equilibrium in a Bargaining Game of Two Sellers and Two Buyers" Mathematics 10, no. 15: 2705. https://doi.org/10.3390/math10152705

APA Style

Li, J., Cui, T., & Kendall, G. (2022). Equilibrium in a Bargaining Game of Two Sellers and Two Buyers. Mathematics, 10(15), 2705. https://doi.org/10.3390/math10152705

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