Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 0000-00-00
Number: 09-038/1
Author-Name: René van den Brink
Author-Workplace-Name: VU University Amsterdam
Author-Name: Gerard van der Laan
Author-Workplace-Name: VU University Amsterdam
Author-Name: Valeri Vasil'ev
Author-Workplace-Name: Sobolev Institute of Mathematics, Russia
Title: The Restricted Core for Totally Positive Games with Ordered Players
Abstract: 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 'dividends' 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.
Classification-JEL: C71
Keywords: Totally positive TU-game, Harsanyi dividends, Core, Shapley value, Harsanyi set, Selectope, Digraph, River game
File-Url: https://papers.tinbergen.nl/09038.pdf
File-Format: application/pdf
File-Size: 369674 bytes
Handle: RePEc:tin:wpaper:20090038