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

Takaaki Abe () and Yukihiko Funaki ()
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Takaaki Abe: Waseda University
Yukihiko Funaki: Waseda University

International Journal of Game Theory, 2017, vol. 46, issue 3, 715-736

Abstract: 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.

Keywords: Cooperative games; Partition function; Core; Externalities (search for similar items in EconPapers)
Date: 2017
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Handle: RePEc:spr:jogath:v:46:y:2017:i:3:d:10.1007_s00182-016-0554-6