The Socially Stable Core in Structured Transferable Utility Games

Arbeitspapier

We consider cooperative games with transferable utility (TU-games), in which we allow for a social structure on the set of players. The social structure is utilized to refine the core of the game. For every coalition the relative strength of a player within that coalition is induced by the social structure and is measured by a power function. We call a payoff vector socially stable if at the collection of coalitions that can attain it, all players have the same power. The socially stable core is the set of socially stable elements of the core. We show that the socially stable core is non-empty if the game itself is socially stable. In general the socially stable core consists of a finite number of faces of the core and generically consists of a finite number of payoff vectors. Convex TU-games have a non-empty socially stable core, irrespective of the power function. When there is a clear hierarchy of players in terms of power, the socially stable core of a convex TU-game consists of exactly one element, an appropriately defined marginal vector. We demonstrate the usefulness of the concept of the socially stable core by two applications. One application concerns sequencing games and the other one the distribution of water.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 04-043/1

Classification and Topics

• Classification: Wirtschaft ; Mathematical Methods; Programming Models; Mathematical and Simulation Modeling: General ; Game Theory and Bargaining Theory: General ; Analysis of Collective Decision-Making: General
• Subject: Transferable Utility game ; Social structure ; Balancedness ; Core ; Kooperatives Spiel ; Transferable Utility Games ; Sozialstruktur ; Core

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Herings, P. Jean-Jacques ; van der Laan, Gerard ; Talman, Dolf
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2004

Further information

• Handle: http://hdl.handle.net/10419/86488
• Last update: 10.03.2025, 11:45 AM CET