The non-emptiness of the core of a partition function form game

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4 Citations (Scopus)

Abstract

The purpose of this paper is to provide a necessary and sufficient condition for the non-emptiness of the core for partition function form games. We generalize the Bondareva–Shapley condition to partition function form games and present the condition for the non-emptiness of “the pessimistic core”, and “the optimistic core”. The pessimistic (optimistic) core describes the stability in assuming that players in a deviating coalition anticipate the worst (best) reaction from the other players. In addition, we define two other notions of the core based on exogenous partitions. The balanced collections in partition function form games and some economic applications are also provided.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalInternational Journal of Game Theory
DOIs
Publication statusAccepted/In press - 2016 Oct 11

Fingerprint

Partition Function
Game
Coalitions
coalition
Partition
Economics
Necessary Conditions
Generalise
Sufficient Conditions
present
economics
Form
Game form

Keywords

  • Cooperative games
  • Core
  • Externalities
  • Partition function

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this

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AB - The purpose of this paper is to provide a necessary and sufficient condition for the non-emptiness of the core for partition function form games. We generalize the Bondareva–Shapley condition to partition function form games and present the condition for the non-emptiness of “the pessimistic core”, and “the optimistic core”. The pessimistic (optimistic) core describes the stability in assuming that players in a deviating coalition anticipate the worst (best) reaction from the other players. In addition, we define two other notions of the core based on exogenous partitions. The balanced collections in partition function form games and some economic applications are also provided.

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