Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2010-07-08 Number: 10-065/1 Author-Name: Rene van den Brink Author-Workplace-Name: VU University Amsterdam, the Netherlands Author-Name: Yukihiko Funaki Author-Workplace-Name: Waseda University Tokyo, Japan Title: Axiomatization and Implementation of Discounted Shapley Values Abstract: This discussion paper resulted in a publication in 'Social Choice and Welfare'.
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. Classification-JEL: C71, C72 Keywords: Cooperative TU-game, Shapley value, equal division solution, delta-discounted Shapley value, Axiomatization, Implementation, Discounting File-Url: http://papers.tinbergen.nl/10065.pdf File-Format: application/pdf File-Size: 273707 bytes Handle: RePEc:tin:wpaper:20100065