Geodesic
The lexicogfraphic prekernel
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 3, pp. 88-114

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The lexicographic prekernel of a cooperative game with transferable utilities (TU) is a subset of the payoff vectors lexicographically minimizing the vector of maximal surpluses of one player over another one. This solution is non-empty for every TU game, it is efficient, is contained both in the prekernel and in the least core, and may not contain the prenucleolus [9]. A combinatorial characterization of the lexicographic prekernel being a weak analog of the known characterization of the prenucleolus by Kohlberg [4] with the help of balanced collections of coalitions is given. The difference consists in sets of vectors to be lexicographic minimized: the prenucleolus deals with excess vectors, and the lexicographi prekernel deals with vectors of maximal surpluses. It is shown that finding the lexicographic prekernel comes to solving a finite set (not more than the number of players) of optimization and of combinatorial problems.
Keywords: cooperative game, prenucleolus, lexicographic prekernel.
Mots-clés : solution, prekernel 
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     author = {Elena B. Yanovskaya},
     title = {The lexicogfraphic prekernel},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {88--114},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2013_5_3_a4/}
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Elena B. Yanovskaya. The lexicogfraphic prekernel. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 5 (2013) no. 3, pp. 88-114. http://geodesic.mathdoc.fr/item/MGTA_2013_5_3_a4/