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Characterizing Compromise Stability of Games Using Larginal Vectors

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Author Info

  • Platz, T.T.
  • Hamers, H.J.M.
  • Quant, M.

    (Tilburg University, Center for Economic Research)

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 order of the players and describes the efficient payoff vector giving the first players in the order 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. In this paper we describe two ways of characterizing sets of larginal vectors that satisfy the condition that if every larginal vector of the set is a core element, then the game is compromise stable. The first characterization of these sets is based on a neighbor argument on orders of the players. The second one uses combinatorial and matching arguments and leads to a complete characterization of these sets. We find characterizing sets of minimum cardinality, a closed formula for the minimum number of orders in these sets, and a partition of the set of all orders in which each element of the partition is a minimum characterizing set.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-058.

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Date of creation: 2011
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Handle: RePEc:dgr:kubcen:2011058

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Web page: http://center.uvt.nl

Related research

Keywords: Core; core cover; larginal vectors; matchings;

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References

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  1. Velzen, S. van & Hamers, H.J.M. & Norde, H.W., 2002. "Convexity and Marginal Vectors," Discussion Paper 2002-53, Tilburg University, Center for Economic Research.
  2. Velzen, S. van & Hamers, H.J.M. & Norde, H.W., 2003. "Characterizing Convexity of Games using Marginal Vectors," Discussion Paper 2003-11, Tilburg University, Center for Economic Research.
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Cited by:
  1. Arantza Est�vez-Fern�ndez & Mar�a Gloria Fiestras-Janeiro & Manuel Alfredo Mosquera & Estela S�nchez- Rodr�guez, 2012. "A Bankruptcy Approach to the Core Cover," Tinbergen Institute Discussion Papers 12-012/1, Tinbergen Institute.
  2. A. Estévez-Fernández & M. Fiestras-Janeiro & M. Mosquera & E. Sánchez-Rodríguez, 2012. "A bankruptcy approach to the core cover," Computational Statistics, Springer, vol. 76(3), pages 343-359, December.
  3. Arantza Est�vez-Fern�ndez & Mar�a Gloria Fiestras-Janeiro & Manuel Alfredo Mosquera & Estela S�nchez- Rodr�guez, 2012. "A Bankruptcy Approach to the Core Cover," Tinbergen Institute Discussion Papers 12-012/1, Tinbergen Institute.

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