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1.
Hsien-Chung Wu 《Fuzzy Optimization and Decision Making》2012,11(1):47-72
Many kinds of proper cores and dominance cores of fuzzy games are proposed in this paper. We also consider two similar concepts
of payoff of a fuzzy coalition that are called the true payoff and quasi-payoff. The different concepts of proper cores and
dominance cores will be proposed based on the true payoff and quasi-payoff of a fuzzy coalition. Some mild sufficient conditions
are provided in this paper to guarantee the equalities of different proper cores and dominance cores. 相似文献
2.
We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (Problemy Kibernet 10:119–139, 1963) and Shapley (Naval Res Logist Q 14: 453–460, 1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that any fuzzy game has a non-empty core if and only if it is balanced. We also consider deposit games to illustrate the use of the main result. 相似文献
3.
T. S. H. Driessen 《Mathematical Methods of Operations Research》1986,30(1):A49-A64
For any natural numbersk andn, the subclass ofk-convexn-person games is introduced. In casek=n, the subclass consists of the convexn-person games. Ak-convexn-person game is characterized in several ways in terms of the core and certain marginal worth vectors. The marginal worth vectors of a game are described in terms of an upper bound for the core and the corresponding gap function. It is shown that thek-convexity of ann-person gamev is equivalent to
- all marginal worth vectors ofv belong to the core ofv; or
- the core ofv is the convex hull of the set consisting of all marginal worth vectors ofv; or
- the extreme points of the core ofv are exactly the marginal worth vectors ofv.
4.
Let A be a group. What can be said about the group B to ensure that A and the normal product AB belong to the same prescribed class of groups? Results in this direction are given for the classes of supersolvable groups, absolutely solvable groups and Lagrange groups. 相似文献
5.
We study competition between an original equipment manufacturer (OEM) and an independently operating remanufacturer (IO). Different from the existing literature, the OEM and IO compete not only for selling their products but also for collecting returned products (cores) through their acquisition prices. We consider a two-period model with manufacturing by the OEM in the first period, and manufacturing as well as remanufacturing in the second period. We find the optimal policies for both players by establishing a Nash equilibrium in the second period, and then determine the optimal manufacturing decision for the OEM in the first period. This leads to a number of managerial insights. One interesting result is that the acquisition price of the OEM only depends on its own cost structure, and not on the acquisition price of the IO. Further insights are obtained from a numerical investigation. We find that when the cost benefits of remanufacturing diminishes and the IO has more chance to collect the available cores, the OEM manufactures less in the first period as the market in the second period gets larger to protect its market share. Finally, we consider the case where consumers have lower willingness to pay for the remanufactured products and find that in that case remanufacturing becomes less profitable overall. 相似文献
6.
We give general conditions, based on the largeness of the core, under which cores of exact TU games are their unique von Neumann-Morgenstern stable sets. We show that this condition is satisfied by convex games and by nonatomic exact market games. In this way, we extend and unify earlier results existing in literature. Under some additional conditions we also prove the equivalence between the core and the Mas-Colell bargaining set.We thank Jean-Francois Mertens, Enrico Minelli, William Thomson, and two anonymous referees for helpful comments. We also thank seminar audiences at CORE, Cornell, Pescara, and Rochester. We gratefully acknowledge the financial support of the Ministero dell’Istruzione, dell’Universitá e della Ricerca. 相似文献
7.
Let \(\gcd (a,b)=1\). J. Olsson and D. Stanton proved that the maximum number of boxes in a simultaneous (a, b)-core is and that this maximum is achieved by a unique core. P. Johnson combined Ehrhart theory with the polynomial method to prove D. Armstrong’s conjecture that the expected number of boxes in a simultaneous (a, b)-core is We extend Johnson’s method to compute the variance to be and also prove polynomiality of all moments. By extending the definitions of “simultaneous cores” and “number of boxes” to affine Weyl groups, we give uniform generalizations of all three formulae above to simply laced affine types. We further explain the appearance of the number 24 using the “strange formula” of H. Freudenthal and H. de Vries.
相似文献
$$\begin{aligned} \max _{\lambda \in {\mathrm {core}}(a,b)} (\mathsf{size}(\lambda )) = \frac{(a^2-1)(b^2-1)}{24} \end{aligned}$$
$$\begin{aligned} \mathop {\mathbb {E}}\limits _{\lambda \in {\mathrm {core}}(a,b)}\left( \mathsf{size}(\lambda )\right) = \frac{(a-1)(b-1)(a+b+1)}{24}. \end{aligned}$$
$$\begin{aligned} \mathop {\mathbb {V}}\limits _{\lambda \in {\mathrm {core}}(a,b)}\left( \mathsf{size}(\lambda )\right) = \frac{ab(a-1)(b-1)(a+b)(a+b+1)}{1440}, \end{aligned}$$
8.
9.
Megumi Harada Nicholas Proudfoot 《Transactions of the American Mathematical Society》2005,357(4):1445-1467
Given an -tuple of positive real numbers , Konno (2000) defines the hyperpolygon space , a hyperkähler analogue of the Kähler variety parametrizing polygons in with edge lengths . The polygon space can be interpreted as the moduli space of stable representations of a certain quiver with fixed dimension vector; from this point of view, is the hyperkähler quiver variety defined by Nakajima. A quiver variety admits a natural -action, and the union of the precompact orbits is called the core. We study the components of the core of , interpreting each one as a moduli space of pairs of polygons in with certain properties. Konno gives a presentation of the cohomology ring of ; we extend this result by computing the -equivariant cohomology ring, as well as the ordinary and equivariant cohomology rings of the core components.
10.
Dr. W. W. Sharkey 《International Journal of Game Theory》1982,11(3-4):175-182
A payoff vector in ann-person cooperative game is said to be acceptable if no coalition can improve upon it. The core of a game consists of all acceptable vectors which are feasible for the grand coalition. The core is said to be large if for every acceptable vectory there is a vectorx in the core withx?y. This paper examines the class of games with large cores. 相似文献
11.
T. Quint PhD. 《International Journal of Game Theory》1991,19(4):413-420
We consider the assignment game of Shapley and Shubik (1972). We prove that the class of possible cores of such games (expressed in terms of payoffs for players on one side of the market) is exactly the same as a special class of polytopes, called 45-lattices. These results parallel similar work done by Conway (in Knuth, 1976) and Blair (1984) for marriage markets.Research supported by the Office of Naval Technology. 相似文献
12.
We prove that the sequence of eigencones (i.e., cones of nonnegative eigenvectors) of positive powers Ak of a nonnegative square matrix A is periodic both in max algebra and in nonnegative linear algebra. Using an argument of Pullman, we also show that the Minkowski sum of the eigencones of powers of A is equal to the core of A defined as the intersection of nonnegative column spans of matrix powers, also in max algebra. Based on this, we describe the set of extremal rays of the core. 相似文献
13.
14.
H. Moulin 《International Journal of Game Theory》1990,19(2):219-232
In a TU cooperative game with populationN, a monotonic core allocation allocates each surplusv (S) among the agents of coalitionS in such a way that agenti's share never decreases when the coalition to which he belongs expands.We investigate the property of largeness (Sharkey [1982]) for monotonic cores. We show the following result. Given a convex TU game and an upper bound on each agent' share in each coalition containing him, if the upper bound depends only upon the size of the coalition and varies monotonically as the size increases, then there exists a monotonic core allocation meeting this system of upper bounds. We apply this result to the provision of a public good problem. 相似文献
15.
16.
Jørn B. Olsson 《Journal of Combinatorial Theory, Series A》2009,116(3):733-740
If s and t are relatively prime positive integers we show that the s-core of a t-core partition is again a t-core partition. A similar result is proved for bar partitions under the additional assumption that s and t are both odd. 相似文献
17.
This paper is devoted to the relations among affine symmetric spaces, smooth Bol and Moufang loops, smooth left distributive
quasigroups and differentiable 3-nets. The results are used to prove the analyticity of smooth Moufang loops and left distributive
quasigroups with involutive left translations as well as to show the Lie nature of transformation groups naturally related
to some classes of smooth binary systems and 3-nets. In the last section we establish power series expansion for local loops
with weak associativity conditions and apply the methods of the previous sections in order to describe geodesic loops having
euclidean lines either as their geodesic lines or as geodesic lines of their core.
The first author was partly supported by the Deutsche Forschungsgemeinschaft and by OTKA Grant no. T020545. 相似文献
18.
Pu Gao 《Random Structures and Algorithms》2015,47(2):341-360
In this paper, we show that in the random graph , with high probability, there exists an integer such that a subgraph of , whose vertex set differs from a densest subgraph of by vertices, is sandwiched by the and the ‐core, for almost all sufficiently large c. We determine the value of . We also prove that (a), the threshold of the k‐core being balanced coincides with the threshold that the average degree of the k‐core is at most , for all sufficiently large k; (b) with high probability, there is a subgraph of whose density is significantly denser than any of its nonempty cores, for almost all sufficiently large c > 0. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 341–360, 2015 相似文献
19.
Marko Orel 《Journal of Algebraic Combinatorics》2012,35(4):633-647
It is shown that the graph Γ
n
that has the set of all n×n symmetric matrices over a finite field as the vertex set, with two matrices being adjacent if and only if the rank of their
difference equals one, is a core if n≥3. Eigenvalues of the graph Γ
n
are calculated as well. 相似文献
20.
The competitive outcomes of an economic system are known, under quite general conditions, always to lie in the core of the associated cooperative game. It is shown here that every “market game” (i.e., one that arises from an exchange economy with money) can be represented by a “direct market” whose competitive outcomes completely fill up the core. It is also shown that it can be represented by a market having any given core outcome as itsunique competitive outcome, or, more generally, having any given compact convex subset of the core as its full set of competitive outcomes. 相似文献