Convexity properties for interior operator games

Convexity properties for interior operator games

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Article ID: iaor2009579
Country: Netherlands
Volume: 158
Issue: 1
Start Page Number: 117
End Page Number: 131
Publication Date: Feb 2008
Journal: Annals of Operations Research
Authors: , , ,
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 an earlier paper 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.

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