The Restricted Core for Totally Positive Games with Ordered Players

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 09-038/1

Classification and Topics

• Classification: Wirtschaft ; Cooperative Games
• Subject: Totally positive TU-game ; Harsanyi dividends ; Core ; Shapley value ; Harsanyi set ; Selectope ; Digraph ; River game ; Transferable Utility Games ; Core ; Shapley-Wert ; Verhandlungstheorie ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): van den Brink, René ; van der Laan, Gerard ; Vasil'ev, Valeri
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2009

Further information

• Handle: http://hdl.handle.net/10419/86809
• Last update: 10.03.2025, 11:45 AM CET