Axiomatization and Implementation of Discounted Shapley Values

Arbeitspapier

We generalize the null player property (satisfied by the Shapley value) and nullifying player property (satisfied by the equal division solution) to the so-called delta-reducing player property, stating that a delta-reducing player (being a player such that any coalition containing this player earns a fraction delta in [0,1] of the worth of that coalition without that player) earns a zero payoff. This property yields the null player property for delta = 1 and the nullifying player property for delta = 0. We show that efficiency, symmetry, linearity and this delta-reducing player property characterizes the corresponding delta-discounted Shapley value. Moreover, we provide a strategic implementation of these solutions where delta is a discount factor that determines the decrease in value to be distributed in the next round after the proposal is rejected and the remaining players (without the proposer) play a new round of bidding.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 10-065/1

Classification and Topics

• Classification: Wirtschaft ; Cooperative Games ; Noncooperative Games
• Subject: Cooperative TU-game ; Shapley value ; equal division solution ; delta-discounted Shapley value ; Axiomatization ; Implementation ; Discounting ; Transferable Utility Games ; Shapley-Wert ; Kooperatives Spiel ; Nichtkooperatives Spiel ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): van den Brink, Rene ; Funaki, Yukihiko
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2010

Further information

• Handle: http://hdl.handle.net/10419/87079
• Last update: 10.03.2025, 11:42 AM CET