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let n 1 2 3 4 write down a list of conditions guaranteeing that in the coalitional structure n player 1 has no
the gloves game two sellers go to the market each has a left-hand glove at the same time three other sellers come to
my aunt and i auntie betty can complete a certain job together with me or with any of my three brothers with the
1 find a two-player coalitional game n v and a v -shaped set k ie a set that is the union of two line segments sharing
prove that the nucleolus is covariant under strategic equivalence for every coalitional game n v for every set k sube
compute the nucleolus and the prenucleolus of the three-player coalitional game n v in which v1 2 1 and vs 0 for
let n v be the three-player coalitional game with the following coalitional functionvs 0 larrrarr s le 1 20208vs 1
compute the prenucleolus of the three-player coalitional game with the following coalitional functionv1 v2 v3 v2 3
player i in a coalitional game n v is a dummy player ifvs cup inbsp vs vi foralls sube niprove that if player i is a
let n v be a coalitional game satisfying the following property there is an imputation x isin xn v such that all the
a find a two-player coalitional game n v and a bounded set k that is not closed such that the nucleolus n n v k is the
a prove that in the gloves game example 203 the imputation y 0 0 1 satisfies thetay l thetau for every u isin xn v u
in this exercise we present an algorithm for computing a solution concept given a coalitional game n va choose a
let n v and n w be two coalitional games satisfying vn wn and vs ge ws for every coalition s sube n prove or disprove
let n v be a coalitional game with a coalitional structure blet k and l be two players who are members of different
prove that a subgame of a convex game is a convex game deduce that every subgame of a convex game has a nonempty core
prove that a three-player 0-normalized game whose core is nonempty and satisfying vs ge 0 for every coalition s is
let d be a balanced collection of coalitions suppose that there is a player i contained in every coalition in d prove
a is the three-player game n v in which v is given by monotonic justify your answerv1 3v2 13v3 4v12 12v13 15v23
a how many different coalitional structures can there be in a three-player game write down all of themb how many
prove that for every coalitional game n v there exists a coalitional structure b for which the set of imputations xb v
a write down the set of imputations of the three-player game in whichv1 3v2 5v3 7v12 6v13 12v23 15v123 10for all
let n v and n w be two coalitional games with the same set of playerslet x isin xb v and y isin xb w does x y isin xb
suppose that you are given an equilateral triangle with x being a point in the triangle denote by x1 x2 x3nbspthe
a give an example of a three-player coalitional game whose core is a triangleb give an example of a three-player