Equilibrium in a Bargaining Game of Two Sellers and Two Buyers

Jiawei Li, Tianxiang Cui and Graham Kendall
Additional contact information
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

Mathematics, 2022, vol. 10, issue 15, 1-9

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/15/2705/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/15/2705/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:15:p:2705-:d:876615

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().