Cooperative games with restricted formation of coalitions

Gleb Koshevoy, Takamasa Suzuki, Dolf Talman

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In the study of cooperative games, restricted cooperation between players is typically modeled by a set system of feasible coalitions of the players. In this paper, we go one step further and allow for a distinction among players within a feasible coalition, between those who are able to form the coalition and those who are not. This defines a contracting map, a choice function. We introduce the notion of quasi-building system and require that such a choice function gives rise to a quasi-building system. Many known set systems and structures studied in the literature are covered by quasi-building systems. For transferable utility games having a quasi-building system as cooperation structure we take as a
solution the average of the marginal vectors that correspond to the set of rooted trees that are compatible with the quasi-building system. Properties of this solution, called the AMV-value, are studied. Relations with other solutions in the literature are also studied. To establish that the AMV-value is an element of the core, we introduce appropriate convexity-type conditions for the game with respect to the underlying quasi-building system. In case of universal cooperation, the AMV-value coincides with the Shapley value.
LanguageEnglish
Article number218
Pages1-13
JournalDiscrete Applied Mathematics
Volume218
DOIs
StatePublished - Feb 2017

Fingerprint

Cooperative Game
Coalitions
Choice Function
Set Systems
Game
Shapley Value
Rooted Trees
Convexity

Keywords

  • set system
  • rooted tree
  • core
  • convexity
  • marginal vector
  • Shapley value

Cite this

Koshevoy, Gleb ; Suzuki, Takamasa ; Talman, Dolf. / Cooperative games with restricted formation of coalitions. In: Discrete Applied Mathematics. 2017 ; Vol. 218. pp. 1-13
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Cooperative games with restricted formation of coalitions. / Koshevoy, Gleb; Suzuki, Takamasa; Talman, Dolf.

In: Discrete Applied Mathematics, Vol. 218, 218, 02.2017, p. 1-13.

Research output: Contribution to journalArticleScientificpeer-review

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AB - In the study of cooperative games, restricted cooperation between players is typically modeled by a set system of feasible coalitions of the players. In this paper, we go one step further and allow for a distinction among players within a feasible coalition, between those who are able to form the coalition and those who are not. This defines a contracting map, a choice function. We introduce the notion of quasi-building system and require that such a choice function gives rise to a quasi-building system. Many known set systems and structures studied in the literature are covered by quasi-building systems. For transferable utility games having a quasi-building system as cooperation structure we take as asolution the average of the marginal vectors that correspond to the set of rooted trees that are compatible with the quasi-building system. Properties of this solution, called the AMV-value, are studied. Relations with other solutions in the literature are also studied. To establish that the AMV-value is an element of the core, we introduce appropriate convexity-type conditions for the game with respect to the underlying quasi-building system. In case of universal cooperation, the AMV-value coincides with the Shapley value.

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