The core of a game with a continuum of players and finite coalitions: The model and some results

Mamoru Kaneko, Myrna Holtz Wooders

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

In this paper we develop a new model of a cooperative game with a continuum of players. In our model, only finite coalitions - ones containing only finite numbers of players - are permitted to form. Outcomes of cooperative behavior are attainable by partitions of the players into finite coalitions: this is appropriate in view of our restrictions on coalition formation. Once feasible outcomes are properly defined, the core concept is standard - no permissible coalition can improve upon its outcome. We provide a sufficient condition for the nonemptiness of the core in the case where the players can be divided into a finite number of types. This result is applied to a market game and the nonemptiness of the core of the market game is stated under considerably weak conditions (but with finite types). In addition, it is illustrated that the framework applies to assignment games with a continuum of players.

Original languageEnglish
Pages (from-to)105-137
Number of pages33
JournalMathematical Social Sciences
Volume12
Issue number2
DOIs
Publication statusPublished - 1986
Externally publishedYes

Fingerprint

Coalitions
Cooperative Behavior
coalition
Continuum
Game
cooperative behavior
coalition formation
market
Coalition Formation
Cooperative Game
Finite Type
Model
Assignment
Partition
Restriction
Continuum of players
Sufficient Conditions
Market games
Market

Keywords

  • Continuum of players
  • f-core
  • finite coalitions
  • game in characteristic function form
  • measure-consistent partitions

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Economics and Econometrics

Cite this

The core of a game with a continuum of players and finite coalitions : The model and some results. / Kaneko, Mamoru; Wooders, Myrna Holtz.

In: Mathematical Social Sciences, Vol. 12, No. 2, 1986, p. 105-137.

Research output: Contribution to journalArticle

@article{2efb794e1c4548e9bd469ac25a5c22bd,
title = "The core of a game with a continuum of players and finite coalitions: The model and some results",
abstract = "In this paper we develop a new model of a cooperative game with a continuum of players. In our model, only finite coalitions - ones containing only finite numbers of players - are permitted to form. Outcomes of cooperative behavior are attainable by partitions of the players into finite coalitions: this is appropriate in view of our restrictions on coalition formation. Once feasible outcomes are properly defined, the core concept is standard - no permissible coalition can improve upon its outcome. We provide a sufficient condition for the nonemptiness of the core in the case where the players can be divided into a finite number of types. This result is applied to a market game and the nonemptiness of the core of the market game is stated under considerably weak conditions (but with finite types). In addition, it is illustrated that the framework applies to assignment games with a continuum of players.",
keywords = "Continuum of players, f-core, finite coalitions, game in characteristic function form, measure-consistent partitions",
author = "Mamoru Kaneko and Wooders, {Myrna Holtz}",
year = "1986",
doi = "10.1016/0165-4896(86)90032-6",
language = "English",
volume = "12",
pages = "105--137",
journal = "Mathematical Social Sciences",
issn = "0165-4896",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - The core of a game with a continuum of players and finite coalitions

T2 - The model and some results

AU - Kaneko, Mamoru

AU - Wooders, Myrna Holtz

PY - 1986

Y1 - 1986

N2 - In this paper we develop a new model of a cooperative game with a continuum of players. In our model, only finite coalitions - ones containing only finite numbers of players - are permitted to form. Outcomes of cooperative behavior are attainable by partitions of the players into finite coalitions: this is appropriate in view of our restrictions on coalition formation. Once feasible outcomes are properly defined, the core concept is standard - no permissible coalition can improve upon its outcome. We provide a sufficient condition for the nonemptiness of the core in the case where the players can be divided into a finite number of types. This result is applied to a market game and the nonemptiness of the core of the market game is stated under considerably weak conditions (but with finite types). In addition, it is illustrated that the framework applies to assignment games with a continuum of players.

AB - In this paper we develop a new model of a cooperative game with a continuum of players. In our model, only finite coalitions - ones containing only finite numbers of players - are permitted to form. Outcomes of cooperative behavior are attainable by partitions of the players into finite coalitions: this is appropriate in view of our restrictions on coalition formation. Once feasible outcomes are properly defined, the core concept is standard - no permissible coalition can improve upon its outcome. We provide a sufficient condition for the nonemptiness of the core in the case where the players can be divided into a finite number of types. This result is applied to a market game and the nonemptiness of the core of the market game is stated under considerably weak conditions (but with finite types). In addition, it is illustrated that the framework applies to assignment games with a continuum of players.

KW - Continuum of players

KW - f-core

KW - finite coalitions

KW - game in characteristic function form

KW - measure-consistent partitions

UR - http://www.scopus.com/inward/record.url?scp=38249039756&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249039756&partnerID=8YFLogxK

U2 - 10.1016/0165-4896(86)90032-6

DO - 10.1016/0165-4896(86)90032-6

M3 - Article

AN - SCOPUS:38249039756

VL - 12

SP - 105

EP - 137

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

IS - 2

ER -