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 language | English |
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Article number | 2705 |
Journal | Mathematics |
Volume | 10 |
Issue number | 15 |
DOIs | |
Publication status | Published - Aug 2022 |
Keywords
- Nash bargaining equilibrium
- bargaining
- bargaining game of two sellers and two buyers
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- General Mathematics
- Engineering (miscellaneous)