Null or Zero Players: The Difference between the Shapley Value and the Egalitarian Solution
AbstractA situation in which a finite set of players can generate certain payoffs by cooperation can be described by a cooperative game with transferable utility. A solution for TU-games assigns to every TU-game a distribution of the payoffs that can be earned over the individual players. Two well-known solutions for TU-games are the Shapley value and the egalitarian solution. The Shapley value is characterized in various ways. Most characterizations use some axiom related to null players, i.e. players who contribute nothing to any coalition. We show that in these characterizations, replacing null players by zero players characterizes the egalitarian solution, where a player is a zero player if every coalition containing this player earns zero worth. We illustrate this difference between these two solutions by applying them to auction games.
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 04-127/1.
Date of creation: 19 Nov 2004
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Null players; zero players; Shapley value; egalitarian solution; strong monotonicity; coalitional monotonicity; auction games;
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-11-30 (All new papers)
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