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In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without
changing the core of the game. These games will be called buyer-seller exact games and satisfy the condition that each mixed-pair
coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyer-seller
exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization
of those assignment games which are buyer-seller exact in terms of the assignment matrix, attainable upper and lower core
bounds for the mixed-pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical
representation of a “45o-lattice” by means of the core of an assignment game can now be answered.
Received: March 2002/Revised version: January 2003
RID="*"
ID="*" Institutional support from research grants BEC 2002-00642 and SGR2001-0029 is gratefully acknowledged
RID="**"
ID="**" The authors thank the referees for their comments 相似文献
3.
Chang [1991] stated some inclusion relation about kernel, reasonable set, and ε-core of games with coalition structure. We
give counterexamples and modify erroneous results.
Received: May 1997/Revised version: January 1999 相似文献
4.
Koji Takamiya 《International Journal of Game Theory》2001,30(2):195-207
This paper examines the α-core of strategic games by means of the consistency principle. I provide a new definition of a
reduced game for strategic games. And I define consistency (CONS) and two forms of converse consistency (COCONS and COCONS*) under this definition of reduced games. Then I axiomatize the α-core for families of strategic games with bounded payoff
functions by the axioms CONS, COCONS*, weak Pareto optimality (WPO) and one person rationality (OPR). Furthermore, I show that these four axioms are logically
independent. In proving this, I also axiomatize the α-individually rational solution by CONS, COCONS and OPR for the same
families of games. Here the α-individually rational solution is a natural extension of the classical `maximin' solution.
Received: June 1998/Final version: 6 July 2001 相似文献
5.
A. Jaśkiewicz 《Journal of Optimization Theory and Applications》2009,141(2):321-347
Zero-sum ergodic semi-Markov games with weakly continuous transition probabilities and lower semicontinuous, possibly unbounded,
payoff functions are studied. Two payoff criteria are considered: the ratio average and the time average. The main result
concerns the existence of a lower semicontinuous solution to the optimality equation and its proof is based on a fixed-point
argument. Moreover, it is shown that the ratio average as well as the time average payoff stochastic games have the same value.
In addition, one player possesses an ε-optimal stationary strategy (ε>0), whereas the other has an optimal stationary strategy.
A. Jaśkiewicz is on leave from Institute of Mathematics and Computer Science, Wrocław University of Technology.
This work is supported by MNiSW Grant 1 P03A 01030. 相似文献
6.
Semicontinuity of Solution Mappings of Parametric Generalized Vector Equilibrium Problems 总被引:1,自引:0,他引:1
In this paper, we study the ε-generalized vector equilibrium problem (ε-GVEP) and the ε-extended vector equilibrium problem (ε-EVEP), which can be regarded as approximate problems to the generalized vector equilibrium problems (GVEP). Existence results
for ε-GVEP and ε-EVEP are established. We investigate also the continuity of the solution mappings of ε-GVEP and ε-EVEP. In particular, two results concerning the lower semicontinuity of the solution mappings of ε-GVEP and ε-EVEP are presented.
This research was partially supported by Grant NSC 95-2811-M-110-010. 相似文献
7.
We consider a quadratic cut method based on analytic centers for two cases of convex quadratic feasibility problems. In the
first case, the convex set is defined by a finite yet large number, N, of convex quadratic inequalities. We extend quadratic cut algorithm of Luo and Sun [3] for solving such problems by placing
or translating the quadratic cuts directly through the current approximate center. We show that, in terms of total number
of addition and translation of cuts, our algorithm has the same polynomial worst case complexity as theirs [3]. However, the
total number of steps, where steps consist of (damped) Newton steps, function evaluations and arithmetic operations, required
to update from one approximate center to another is , where ε is the radius of the largest ball contained in the feasible set. In the second case, the convex set is defined by
an infinite number of certain strongly convex quadratic inequalities. We adapt the same quadratic cut method for the first
case to the second one. We show that in this case the quadratic cut algorithm is a fully polynomial approximation scheme.
Furthermore, we show that, at each iteration, k, the total number steps (as described above) required to update from one approximate center to another is at most , with ε as defined above.
Received: April 2000 / Accepted: June 2002 Published online: September 5, 2002
Key words. convex quadratic feasibility problem – interior-point methods – analytic center – quadratic cuts – potential function 相似文献
8.
Robert Samuel Simon 《Israel Journal of Mathematics》2006,156(1):285-309
A stochastic game isvalued if for every playerk there is a functionr
k:S→R from the state spaceS to the real numbers such that for every ε>0 there is an ε equilibrium such that with probability at least 1−ε no states is reached where the future expected payoff for any playerk differs fromr
k(s) by more than ε. We call a stochastic gamenormal if the state space is at most countable, there are finitely many players, at every state every player has only finitely many
actions, and the payoffs are uniformly bounded and Borel measurable as functions on the histories of play. We demonstrate
an example of a recursive two-person non-zero-sum normal stochastic game with only three non-absorbing states and limit average
payoffs that is not valued (but does have ε equilibria for every positive ε). In this respect two-person non-zero-sum stochastic
games are very different from their zero-sum varieties. N. Vieille proved that all such non-zero-sum games with finitely many
states have an ε equilibrium for every positive ε, and our example shows that any proof of this result must be qualitatively
different from the existence proofs for zero-sum games. To show that our example is not valued we need that the existence
of ε equilibria for all positive ε implies a “perfection” property. Should there exist a normal stochastic game without an
ε equilibrium for some ε>0, this perfection property may be useful for demonstrating this fact. Furthermore, our example sews
some doubt concerning the existence of ε equilibria for two-person non-zero-sum recursive normal stochastic games with countably
many states.
This research was supported financially by the German Science Foundation (Deutsche Forschungsgemeinschaft) and the Center
for High Performance Computing (Technical University, Dresden). The author thanks Ulrich Krengel and Heinrich Hering for their
support of his habilitation at the University of Goettingen, of which this paper is a part. 相似文献
9.
In this paper we address bargaining games where the agents have to take into account different criteria to value the decisions.
We propose the class of generalized maximin solutions, as the natural extension for these games of the maximin solutions in
conventional bargaining. In order to refine this solution concept, we define a multicriteria lexicographic partial ordering
and present the class of generalized leximin solutions as those that are nondominated with respect to this relation. We establish
some properties of these solutions and characterize them as solutions of multicriteria problems.
The research of the authors is partially supported by the Spanish Ministry of Science and Technology projects BFM2002-11282-E
and BEC2003-03111. 相似文献
10.
A note on the nucleolus and the kernel of the assignment game 总被引:1,自引:0,他引:1
There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyer–seller exact representative.I am grateful to C. Rafels and to the referees for their comments. Institutional support from research grants BEC 2002-00642 and SGR2001–0029 is also acknowledged. 相似文献
11.
On the validity of the Ginzburg-Landau equation 总被引:1,自引:0,他引:1
A. van Harten 《Journal of Nonlinear Science》1991,1(4):397-422
Summary The famous Ginzburg-Landau equation describes nonlinear amplitude modulations of a wave perturbation of a basic pattern when
a control parameterR lies in the unstable regionO(ε
2) away from the critical valueR
c for which the system loses stability. Hereε>0 is a small parameter. G-L's equation is found for a general class of nonlinear evolution problems including several classical
problems from hydrodynamics and other fields of physics and chemistry. Up to now, the rigorous derivation of G-L's equation
for general situations is not yet completed. This was only demonstrated for special types of solutions (steady, time periodic)
or for special problems (the Swift-Hohenberg equation). Here a mathematically rigorous proof of the validity of G-L's equation
is given for a general situation of one space variable and a quadratic nonlinearity. Validity is meant in the following sense.
For each given initial condition in a suitable Banach space there exists a unique bounded solution of the initial value problem
for G-L's equation on a finite interval of theO(1/ε2)-long time scale intrinsic to the modulation. For such a finite time interval of the intrinsic modulation time scale on which
the initial value problem for G-L's equation has a bounded solution, the initial value problem for the original evolution
equation with corresponding initial conditions, has a unique solutionO(ε2) — close to the approximation induced by the solution of G-L's equation. This property guarantees that, for rather general
initial conditions on the intrinsic modulation time scale, the behavior of solutions of G-L's equation is really inherited
from solutions of the original problem, and the other way around: to a solution of G-L's equation corresponds a nearby exact
solution with a relatively small error. 相似文献
12.
Victor Domansky 《International Journal of Game Theory》2007,36(2):241-257
This paper is concerned with multistage bidding models introduced in De Meyer and Moussa Saley (Int J Game Theory 31:285–319,
2002) to analyze the evolution of the price system at finance markets with asymmetric information. The repeated games are
considered modelling the biddings with the admissible bids k/m, unlike the above mentioned paper, where arbitrary bids are allowed. It is shown that the sequence of values of n-step games is bounded from above and converges to the value of the game with infinite number of steps. The optimal strategies
of infinite game generate a symmetric random walk of transaction prices over admissible bids with absorbing extreme points.
The value of infinite game is equal to the expected duration of this random walk multiplied by the constant one-step gain
of informed Player 1.
This study was supported by the grant 04-06-80430 of Russian Foundation of Basic Research which is gratefully acknowledged.
I am thankful to anonymous referees and to William Thomson for instructive and helpful remarks and comments. 相似文献
13.
E. Mijangos 《Journal of Optimization Theory and Applications》2006,128(1):167-190
The minimization of nonlinearly constrained network flow problems can be performed by using approximate subgradient methods.
The idea is to solve this kind of problem by means of primal-dual methods, given that the minimization of nonlinear network
flow problems can be done efficiently exploiting the network structure. In this work, it is proposed to solve the dual problem
by using ε-subgradient methods, as the dual function is estimated by minimizing approximately a Lagrangian function, which
includes the side constraints (nonnetwork constraints) and is subject only to the network constraints. Some well-known subgradient
methods are modified in order to be used as ε-subgradient methods and the convergence properties of these new methods are
analyzed. Numerical results appear very promising and effective for this kind of problems
This research was partially supported by Grant MCYT DPI 2002-03330. 相似文献
14.
We consider an infinitely repeated two-person zero-sum game with incomplete information on one side, in which the maximizer
is the (more) informed player. Such games have value v
∞ (p) for all 0≤p≤1. The informed player can guarantee that all along the game the average payoff per stage will be greater than or equal to
v
∞ (p) (and will converge from above to v
∞ (p) if the minimizer plays optimally). Thus there is a conflict of interest between the two players as to the speed of convergence
of the average payoffs-to the value v
∞ (p). In the context of such repeated games, we define a game for the speed of convergence, denoted SG
∞ (p), and a value for this game. We prove that the value exists for games with the highest error term, i.e., games in which v
n (p)− v
∞ (p) is of the order of magnitude of . In that case the value of SG
∞ (p) is of the order of magnitude of . We then show a class of games for which the value does not exist. Given any infinite martingale 𝔛∞={X
k }∞
k=1, one defines for each n : V
n (𝔛∞) ≔E∑n
k=1 |X
k+1 − X
k|. For our first result we prove that for a uniformly bounded, infinite martingale 𝔛∞, V
n (𝔛∞) can be of the order of magnitude of n
1/2−ε, for arbitrarily small ε>0.
Received January 1999/Final version April 2002 相似文献
15.
MIXED FINITE ELEMENT METHOD FOR THE CONVECTION-DOMINATED DIFFUSION PROBLEMS WITH SMALL PARAMETER ε 总被引:2,自引:0,他引:2
CHENHUANZHEN 《高校应用数学学报(英文版)》1998,13(2):199-206
In rids paper a mixed finite element method for the convection-dominated diffusion problems with small parameter ε is presented,the effect of the parameter ε on the approximation error is considered and a sufficient condition for optimal error estimates is derived. The paper also shows that under some conditions,the standard finite dement method only gives a hounded solution,however the mixed finite element method gives a convergent one. 相似文献
16.
Jingang Zhao 《International Journal of Game Theory》1999,28(1):25-34
This paper provides a TU α-core existence result in a large class of normal form games. In the oligopoly markets of a homogeneous
good, the TU α-core is non-empty if all profit functions are continuous and concave. In a general game, the existence of TU
α-core follows from the weak separability, the compactness and convexity of choice sets, and the concavity and continuity
of payoff functions.
Received: November 1997/final version: August 1998 相似文献
17.
T. Q. Son J. J. Strodiot V. H. Nguyen 《Journal of Optimization Theory and Applications》2009,141(2):389-409
In this paper, ε-optimality conditions are given for a nonconvex programming problem which has an infinite number of constraints. The objective
function and the constraint functions are supposed to be locally Lipschitz on a Banach space. In a first part, we introduce
the concept of regular ε-solution and propose a generalization of the Karush-Kuhn-Tucker conditions. These conditions are up to ε and are obtained by weakening the classical complementarity conditions. Furthermore, they are satisfied without assuming
any constraint qualification. Then, we prove that these conditions are also sufficient for ε-optimality when the constraints are convex and the objective function is ε-semiconvex. In a second part, we define quasisaddlepoints associated with an ε-Lagrangian functional and we investigate their relationships with the generalized KKT conditions. In particular, we formulate
a Wolfe-type dual problem which allows us to present ε-duality theorems and relationships between the KKT conditions and regular ε-solutions for the dual. Finally, we apply these results to two important infinite programming problems: the cone-constrained
convex problem and the semidefinite programming problem. 相似文献
18.
19.
Values of games with a continuum of players 总被引:1,自引:0,他引:1
Yakar Kannai 《Israel Journal of Mathematics》1966,4(1):54-58
A definition of the “Shapley value” of games with a continuum of players and a formula for this value are given for a certain
class of games, regarding them as limits of games with a finite number of players.
The research described in this paper was partially supported by the U.S. Office of Naval Research, Logistics and Mathematical
Statistics Branch, under Contract Number N 62558-3586. 相似文献
20.
Santanu S. Dey Jean-Philippe P. Richard Yanjun Li Lisa A. Miller 《Mathematical Programming》2010,121(1):145-170
Infinite group relaxations of integer programs (IP) were introduced by Gomory and Johnson (Math Program 3:23–85, 1972) to
generate cutting planes for general IPs. These valid inequalities correspond to real-valued functions defined over an appropriate
infinite group. Among all the valid inequalities of the infinite group relaxation, extreme inequalities are most important
since they are the strongest cutting planes that can be obtained within the group-theoretic framework. However, very few properties
of extreme inequalities of infinite group relaxations are known. In particular, it is not known if all extreme inequalities
are continuous and what their relations are to extreme inequalities of finite group problems. In this paper, we describe new
properties of extreme functions of infinite group problems. In particular, we study the behavior of the pointwise limit of
a converging sequence of extreme functions as well as the relations between extreme functions of finite and infinite group
problems. Using these results, we prove for the first time that a large class of discontinuous functions is extreme for infinite
group problems. This class of extreme functions is the generalization of the functions given by Letchford and Lodi (Oper Res
Lett 30(2):74–82, 2002), Dash and Günlük (Proceedings 10th conference on integer programming and combinatorial optimization.
Springer, Heidelberg, pp 33–45 (2004), Math Program 106:29–53, 2006) and Richard et al. (Math Program 2008, to appear). We
also present several other new classes of discontinuous extreme functions. Surprisingly, we prove that the functions defining
extreme inequalities for infinite group relaxations of mixed integer programs are continuous.
S.S. Dey and J.-P.P. Richard was supported by NSF Grant DMI-03-48611. 相似文献