TY - BOOK

T1 - The monoclus of a coalitional game

AU - Slikker, M.

AU - Norde, H.W.

PY - 2008

Y1 - 2008

N2 - 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.

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.

M3 - Report

SN - 978-90-386-1217-1

T3 - BETA publicatie : working papers

BT - The monoclus of a coalitional game

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -