The grand dividends value

Besner, Manfred (2021): The grand dividends value.

Abstract

We introduce a new value for games with transferable utility, called grand dividends value. In the payoff calculation, the grand dividends value takes into account the worths of all subcoalitions of a player set. The concept of grand dividends, representing the surplus (which can also be non-positive) of the worth of the grand coalition over the worths of all coalitions that lack one player of the player set, is the initial point here. Many of the properties known from the Shapley value are also satisfied by the grand dividends value. Along with new axioms having a similar correspondence to axioms satisfied by the Shapley value, axiomatizations arise that have an analogous equivalent for the Shapley value, including the classics by Shapley and Young. The new concept of multiple dividends provides a close connection to the Shapley value.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cooperative game; (Harsanyi/Grand/Multiple) Dividends ; Shapley value; Grand dividends value
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

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