The quasi-prekernel for cooperative games

Qianqian Kong; Hans Peters; Hao Sun

doi:10.1016/j.geb.2026.03.009

The quasi-prekernel for cooperative games

Qianqian Kong
, Hans Peters^*
, Hao Sun

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The quasi-prekernel is a novel solution concept for cooperative games. It is a refinement of existing prebargaining set solutions, notably the reactive, semireactive, and Aumann-Davis-Maschler prebargaining sets. It contains the prekernel, and coincides with that solution on simple games except possibly on balanced simple games with all individual worths equal to zero. An axiomatic characterization based on reduced game properties is provided. The steady version, obtained by putting conditions on objecting and counterobjecting coalitions, is considered as well. Finally, by considering objecting and counterobjecting coalitions independent of specific players, the socalled excess prebargaining obtains, which is another novel solution concept.

Original language	English
Pages (from-to)	260-271
Number of pages	12
Journal	Games and Economic Behavior
Volume	158
DOIs	https://doi.org/10.1016/j.geb.2026.03.009
Publication status	Published - 1 Jun 2026

JEL classifications

c71 - Cooperative Games

Keywords

Cooperative game
Quasi-prekernel
Simple game
Reduced game
Excess prebargaining set
REACTIVE BARGAINING SET
POWER
EXISTENCE
NUCLEOLUS
THEOREM
KERNEL

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Cite this

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title = "The quasi-prekernel for cooperative games",

abstract = "The quasi-prekernel is a novel solution concept for cooperative games. It is a refinement of existing prebargaining set solutions, notably the reactive, semireactive, and Aumann-Davis-Maschler prebargaining sets. It contains the prekernel, and coincides with that solution on simple games except possibly on balanced simple games with all individual worths equal to zero. An axiomatic characterization based on reduced game properties is provided. The steady version, obtained by putting conditions on objecting and counterobjecting coalitions, is considered as well. Finally, by considering objecting and counterobjecting coalitions independent of specific players, the socalled excess prebargaining obtains, which is another novel solution concept.",

keywords = "Cooperative game, Quasi-prekernel, Simple game, Reduced game, Excess prebargaining set, REACTIVE BARGAINING SET, POWER, EXISTENCE, NUCLEOLUS, THEOREM, KERNEL",

author = "Qianqian Kong and Hans Peters and Hao Sun",

note = "Data availability No data was used for the research described in the article.",

year = "2026",

month = jun,

day = "1",

doi = "10.1016/j.geb.2026.03.009",

language = "English",

volume = "158",

pages = "260--271",

journal = "Games and Economic Behavior",

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publisher = "Academic Press Inc.",

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TY - JOUR

T1 - The quasi-prekernel for cooperative games

AU - Kong, Qianqian

AU - Peters, Hans

AU - Sun, Hao

N1 - Data availability No data was used for the research described in the article.

PY - 2026/6/1

Y1 - 2026/6/1

N2 - The quasi-prekernel is a novel solution concept for cooperative games. It is a refinement of existing prebargaining set solutions, notably the reactive, semireactive, and Aumann-Davis-Maschler prebargaining sets. It contains the prekernel, and coincides with that solution on simple games except possibly on balanced simple games with all individual worths equal to zero. An axiomatic characterization based on reduced game properties is provided. The steady version, obtained by putting conditions on objecting and counterobjecting coalitions, is considered as well. Finally, by considering objecting and counterobjecting coalitions independent of specific players, the socalled excess prebargaining obtains, which is another novel solution concept.

AB - The quasi-prekernel is a novel solution concept for cooperative games. It is a refinement of existing prebargaining set solutions, notably the reactive, semireactive, and Aumann-Davis-Maschler prebargaining sets. It contains the prekernel, and coincides with that solution on simple games except possibly on balanced simple games with all individual worths equal to zero. An axiomatic characterization based on reduced game properties is provided. The steady version, obtained by putting conditions on objecting and counterobjecting coalitions, is considered as well. Finally, by considering objecting and counterobjecting coalitions independent of specific players, the socalled excess prebargaining obtains, which is another novel solution concept.

KW - Cooperative game

KW - Quasi-prekernel

KW - Simple game

KW - Reduced game

KW - Excess prebargaining set

KW - REACTIVE BARGAINING SET

KW - POWER

KW - EXISTENCE

KW - NUCLEOLUS

KW - THEOREM

KW - KERNEL

U2 - 10.1016/j.geb.2026.03.009

DO - 10.1016/j.geb.2026.03.009

M3 - Article

SN - 0899-8256

VL - 158

SP - 260

EP - 271

JO - Games and Economic Behavior

JF - Games and Economic Behavior

ER -

The quasi-prekernel for cooperative games

Abstract

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Keywords

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