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Analytic solution for the nucleolus of a three‐player cooperative game
Author(s) -
Leng Mingming,
Parlar Mahmut
Publication year - 2010
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.20429
Subject(s) - core (optical fiber) , sequence (biology) , solution concept , function (biology) , nucleolus , mathematics , mathematical economics , algebraic number , value (mathematics) , computer science , mathematical optimization , characteristic function (probability theory) , scale (ratio) , cooperative game theory , game theory , mathematical analysis , physics , probability density function , statistics , telecommunications , biochemistry , chemistry , genetics , quantum mechanics , evolutionary biology , cytoplasm , biology
The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programing (LP) problems, or by solving a single, but very large‐scale, LP problem. This article proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed‐form) for a three‐player cooperative game in characteristic function form. We first consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with nonempty core and calculate the nucleolus solution analytically for five possible cases arising from the relationship among the value functions of different coalitions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010