Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2004-11-19
Number: 04-127/1
Author-Name: René van den Brink
Author-Email: jrbrink@feweb.vu.nl
Author-Workplace-Name: Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam
Title: Null or Zero Players: The Difference between the Shapley Value and the Egalitarian Solution
Abstract: This discussion paper led to a publication in the 'Journal of Economic Theory', 2007, 136, 767-775.

A 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.
Classification-JEL: C71; D44
Keywords: Null players; zero players; Shapley value; egalitarian solution; strong monotonicity; coalitional monotonicity; auction games
File-Url: https://papers.tinbergen.nl/04127.pdf
File-Format: application/pdf
File-Size: 738017 bytes
Handle: RePEc:tin:wpaper:20040127