The Monoclus of a Coalitional Game

M. Slikker, H.W. Norde

Research output: Working paperDiscussion paperOther research output

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages24
Volume2008-6
Publication statusPublished - 2008

Publication series

NameCentER Discussion Paper
Volume2008-6

Keywords

  • cooperative game theory
  • population monotonic allocation schemes
  • allocation scheme rules

Cite this

Slikker, M., & Norde, H. W. (2008). The Monoclus of a Coalitional Game. (CentER Discussion Paper; Vol. 2008-6). Tilburg: Microeconomics.
Slikker, M. ; Norde, H.W. / The Monoclus of a Coalitional Game. Tilburg : Microeconomics, 2008. (CentER Discussion Paper).
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Slikker, M & Norde, HW 2008 'The Monoclus of a Coalitional Game' CentER Discussion Paper, vol. 2008-6, Microeconomics, Tilburg.

The Monoclus of a Coalitional Game. / Slikker, M.; Norde, H.W.

Tilburg : Microeconomics, 2008. (CentER Discussion Paper; Vol. 2008-6).

Research output: Working paperDiscussion paperOther research output

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AB - 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.

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Slikker M, Norde HW. The Monoclus of a Coalitional Game. Tilburg: Microeconomics. 2008. (CentER Discussion Paper).