Equilibrium in a Bargaining Game of Two Sellers and Two Buyers
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...
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2705 |
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| author | Jiawei Li Tianxiang Cui Graham Kendall |
| author_facet | Jiawei Li Tianxiang Cui Graham Kendall |
| author_sort | Jiawei Li |
| collection | DOAJ |
| description | 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 <i>n</i>-sellers and <i>n</i>-buyers, which reveals the relevance of bargaining equilibrium to the general equilibrium of a market. |
| first_indexed | 2024-03-09T12:22:28Z |
| format | Article |
| id | doaj.art-1596d5e4fb4744cdb1293d8f06d8312c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T12:22:28Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1596d5e4fb4744cdb1293d8f06d8312c2023-11-30T22:38:19ZengMDPI AGMathematics2227-73902022-07-011015270510.3390/math10152705Equilibrium in a Bargaining Game of Two Sellers and Two BuyersJiawei Li0Tianxiang Cui1Graham Kendall2School of Computer Science, University of Nottingham Ningbo China, Ningbo 315100, ChinaSchool of Computer Science, University of Nottingham Ningbo China, Ningbo 315100, ChinaSchool of Computer Science, University of Nottingham UK, Nottingham NG7 2RD, UKThe 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 <i>n</i>-sellers and <i>n</i>-buyers, which reveals the relevance of bargaining equilibrium to the general equilibrium of a market.https://www.mdpi.com/2227-7390/10/15/2705bargainingNash bargaining equilibriumbargaining game of two sellers and two buyers |
| spellingShingle | Jiawei Li Tianxiang Cui Graham Kendall Equilibrium in a Bargaining Game of Two Sellers and Two Buyers Mathematics bargaining Nash bargaining equilibrium bargaining game of two sellers and two buyers |
| title | Equilibrium in a Bargaining Game of Two Sellers and Two Buyers |
| title_full | Equilibrium in a Bargaining Game of Two Sellers and Two Buyers |
| title_fullStr | Equilibrium in a Bargaining Game of Two Sellers and Two Buyers |
| title_full_unstemmed | Equilibrium in a Bargaining Game of Two Sellers and Two Buyers |
| title_short | Equilibrium in a Bargaining Game of Two Sellers and Two Buyers |
| title_sort | equilibrium in a bargaining game of two sellers and two buyers |
| topic | bargaining Nash bargaining equilibrium bargaining game of two sellers and two buyers |
| url | https://www.mdpi.com/2227-7390/10/15/2705 |
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