Cooperative Games in Graph Structure

P. Jean-Jacques Herings (), Gerard van der Laan and Dolf Talman ()

No 00-072/1, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: In this paper we generalize the concept of coalitional games by allowing for any organizational structure within coalitions represented by a graph on the set of players ot the coalition. A, possibly empty, set of payoff vectors is assigned to any graph on every subset of players. Such a game will be called a graph game. For each graph a power vector is determined that depends on the relative positions of the players within the graph. A collection of graphs will be called balanced if to any graph in the collection a positive weight can be assigned such that the weighted power vectors sum up to the vector of ones. We then define the balanced-core as a refinement of the core. A payoff vector lies in the balanced-core if it lies in the core and the payoff vector is an element of payoff sets of all graphs in some balanced collection of graphs. We prove that any balanced graph game has a nonempty balanced-core.

We conclude by some examples showing the usefulness of the concepts of graph games and balanced-core. In particular these examples show a close relationship between solutions to noncooperative games and balanced-core elements of a well-defined graph game.

Keywords: cooperative games; graphs; balancedness; core; Nash program (search for similar items in EconPapers)
Date: 2000-08-25
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Related works:
Working Paper: Cooperative games in graph structure (2000)
Working Paper: Cooperative Games in Graph Structure (2000)
Working Paper: Cooperative Games in Graph Structure (2002)
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