 Axiomatization and Implementation of Discounted Shapley ValuesRene van den Brink () and Yukihiko Funaki () No 10-065/1, Tinbergen Institute Discussion Papers from Tinbergen Institute 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. Keywords: Cooperative TU-game; Shapley value; equal division solution; delta-discounted Shapley value; Axiomatization; Implementation; Discounting (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20100065 Access Statistics for this paper More papers in Tinbergen Institute Discussion Papers from Tinbergen Institute Contact information at EDIRC. |
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