Colorful linear programming, Nash equilibrium, and pivots
نویسندگان
چکیده
منابع مشابه
Colorful linear programming, Nash equilibrium, and pivots
The colorful Carathéodory theorem, proved by Bárány in 1982, states that given d+1 sets of points S1, . . . ,Sd+1 in R , such that each Si contains 0 in its convex hull, there exists a set T ⊆ ⋃ d+1 i=1 Si containing 0 in its convex hull and such that |T ∩Si| ≤ 1 for all i ∈ {1, . . . , d + 1}. An intriguing question – still open – is whether such a set T , whose existence is ensured, can be fo...
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Let S1, . . . ,Sk be k sets of points in Qd. The colorful linear programming problem, defined by Bárány and Onn (Mathematics of Operations Research, 22 (1997), 550–567), aims at deciding whether there exists a T ⊆ ⋃k i=1 Si such that |T ∩ Si| ≤ 1 for i = 1, . . . , k and 0 ∈ conv(T ). They proved in their paper that this problem is NP-complete when k = d. They leave as an open question the comp...
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Colorful linear programming (CLP) is a generalization of linear programming that was introduced by Bárány and Onn. Given k point sets C1, . . . , Ck ⊂ R that each contain a point b ∈ R in their positive span, the problem is to compute a set C ⊆ C1 ∪ · · · ∪ Ck that contains at most one point from each set Ci and that also contains b in its positive span, or to state that no such set exists. CLP...
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This paper considers the numerical solution of linear generalized Nash equilibrium problems. Since many methods for nonlinear problems require the nonsingularity of some second order derivative, standard convergence conditions are not satisfied in our linear case. We provide new convergence criteria for a potential reduction algorithm that allow its application to linear generalized Nash equili...
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In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2018
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.10.006