Equilibrium in a Bargaining Game of Two Sellers and Two Buyers

Jiawei Li, Tianxiang Cui, Graham Kendall

Research output: Journal PublicationArticlepeer-review

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.

Original languageEnglish
Article number2705
JournalMathematics
Volume10
Issue number15
DOIs
Publication statusPublished - Aug 2022

Keywords

  • bargaining
  • bargaining game of two sellers and two buyers
  • Nash bargaining equilibrium

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Mathematics (all)
  • Engineering (miscellaneous)

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