Annals of Operations Research

, Volume 158, Issue 1, pp 117–131 | Cite as

Convexity properties for interior operator games

  • J. M. Bilbao
  • C. Chacón
  • A. Jiménez-Losada
  • E. Lebrón
Article

Abstract

Interior operator games arose by abstracting some properties of several types of cooperative games (for instance: peer group games, big boss games, clan games and information market games). This reason allow us to focus on different problems in the same way. We introduced these games in Bilbao et al. (Ann. Oper. Res. 137:141–160, 2005) by a set system with structure of antimatroid, that determines the feasible coalitions, and a non-negative vector, that represents a payoff distribution over the players. These games, in general, are not convex games. The main goal of this paper is to study under which conditions an interior operator game verifies other convexity properties: 1-convexity, k-convexity (k≥2 ) or semiconvexity. But, we will study these properties over structures more general than antimatroids: the interior operator structures. In every case, several characterizations in terms of the gap function and the initial vector are obtained. We also find the family of interior operator structures (particularly antimatroids) where every interior operator game satisfies one of these properties.

Keywords

Cooperative game Antimatroid Interior operator Convexity 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • J. M. Bilbao
    • 1
  • C. Chacón
    • 1
  • A. Jiménez-Losada
    • 1
  • E. Lebrón
    • 1
  1. 1.Matemática Aplicada IIEscuela Superior de IngenierosSevillaSpain

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