The Restricted Core for Totally Positive Games with Ordered Players
René Van den Brink
VU University Amsterdam - Department of Economics; Tinbergen Institute; Tinbergen Institute - Tinbergen Institute Amsterdam (TIA)
Gerard Van der Laan
VU University Amsterdam - Faculty of Economics and Business Administration; Tinbergen Institute - Tinbergen Institute Amsterdam (TIA)
Valeri A. Vasil'ev
Sobolev Institute of Mathematics
April 29, 2009
Tinbergen Institute Discussion Paper 09-038/1
Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many such allocation problems, such as river games, queueing games and auction games, the game is totally positive (i.e., all dividends are nonnegative), and there is some hierarchical ordering of the players. In this paper we introduce the Restricted Core for such games with ordered players which is based on the distribution of taking into account the hierarchical ordering of the players. For totally positive games this solution is always contained in the Core, and contains the well-known Shapley value (being the single-valued solution distributing the dividends equally among the players in the corresponding coalitions). For special orderings it equals the Core, respectively Shapley value. We provide an axiomatization and apply this solution to river games.
Number of Pages in PDF File: 31
Keywords: Totally positive TU-game, Harsanyi dividends, Core, Shapley value, Harsanyi set, Selectope, Digraph, River game
JEL Classification: C71working papers series
Date posted: August 5, 2009
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