C-complete sets for compromise stable games

Trine Platz, Herbert Hamers () and Marieke Quant
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Herbert Hamers: Department of Econometrics & OR and CentER, Postal: Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands

No 25/2012, Discussion Papers on Economics from University of Southern Denmark, Department of Economics

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.

Keywords: Core; core cover; larginal vectors (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 14 pages
Date: 2012-12-03
New Economics Papers: this item is included in nep-gth and nep-mic
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Journal Article: C-complete sets for compromise stable games (2014)
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