The Monoclus of a Coalitional Game

CentER Discussion Paper No. 2008-06

24 Pages Posted: 12 Feb 2008

See all articles by Marco Slikker

Marco Slikker

Eindhoven University of Technology (TUE) - School of Industrial Engineering

Henk Norde

Tilburg University - Center For Economic Research; Tilburg University - Department of Econometrics & Operations Research

Date Written: January 2008

Abstract

The analysis of single-valued solution concepts for coalitional games with transferable utilities has a long tradition. Opposed to most of this literature we will not deal with solution concepts that provide payoffs to the players for the grand coalition only, but we will analyze allocation scheme rules, which assign payoffs to all players in all coalitions. We introduce four closely related allocation scheme rules for coalitional games. Each of these rules results in a population monotonic allocation scheme (PMAS) whenever the underlying coalitional game allows for a PMAS. The driving force behind these rules are monotonicities, which measure the payoff difference for a player between two nested coalitions. From a functional point of view these monotonicities can best be compared with the excesses in the definition of the (pre-)nucleolus. Two different domains and two different collections of monotonicities result in four allocation scheme rules. For each of the rules we deal with nonemptiness, uniqueness, and continuity, followed by an analysis of conditions for (some of) the rules to coincide. We then focus on characterizing the rules in terms of subbalanced weights. Finally, we deal with computational issues by providing a sequence of linear programs.

Keywords: cooperative game theory, population monotonic allocation schemes, allocation

JEL Classification: C71

Suggested Citation

Slikker, Marco and Norde, Henk W., The Monoclus of a Coalitional Game (January 2008). CentER Discussion Paper No. 2008-06, Available at SSRN: https://ssrn.com/abstract=1092416 or http://dx.doi.org/10.2139/ssrn.1092416

Marco Slikker (Contact Author)

Eindhoven University of Technology (TUE) - School of Industrial Engineering ( email )

P.O. Box 513
5600 MB Eindhoven
Netherlands

Henk W. Norde

Tilburg University - Center For Economic Research ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 3245 (Phone)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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