C-complete Sets for Compromise Stable Games

Trine Tornøe Platz, Herbert Hamers, Marieke Quant

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an ordering of the players and describes the efficient payoff vector giving the first players in the ordering their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. This paper analyzes the structure of orderings corresponding to larginal vectors of the core cover and conditions ensuring equality between core cover and core. We introduce compromise complete (or c-complete) sets that satisfy the condition that if every larginal vector corresponding to an ordering of the set is a core element, then the game is compromise stable. We use combinatorial arguments to give a complete characterization of these sets. More specifically, we find c-complete sets of minimum cardinality and a closed formula for the minimum number of orderings in c-complete sets. Furthermore, we discuss the number of different larginal vectors corresponding to a c-complete set of orderings.
Original languageEnglish
JournalMathematical Methods of Operations Research
Volume80
Issue number2
Pages (from-to)213–223
ISSN1432-2994
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Core
  • Core cover
  • Larginal vectors
  • TU-game

Cite this

Platz, Trine Tornøe ; Hamers, Herbert ; Quant, Marieke. / C-complete Sets for Compromise Stable Games. In: Mathematical Methods of Operations Research. 2014 ; Vol. 80, No. 2. pp. 213–223.
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C-complete Sets for Compromise Stable Games. / Platz, Trine Tornøe ; Hamers, Herbert; Quant, Marieke.

In: Mathematical Methods of Operations Research, Vol. 80, No. 2, 2014, p. 213–223.

Research output: Contribution to journalJournal articleResearchpeer-review

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