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.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
file. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number
2008-06.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.: