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

Mamoru Kaneko, Myrna Holtz Wooders

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55 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1986
Externally publishedYes



  • 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

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