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1.
我们将在Ramik定义的模糊最大序关系基础上研究模糊环境中的二人零和对策。在非对称模糊数基础上,引入模糊环境中的几种Nash均衡策略,讨论各种均衡策略存在的充要条件。并引入含参变量确定性矩阵对策及其均衡策略的概念,讨论含参变量确定性矩阵对策的Nash均衡策略和模糊值矩阵对策的均衡策略的关系。 相似文献
2.
一般化两人零和模糊对策的模糊规划法 总被引:1,自引:0,他引:1
本文在充分考虑局中人的策略集是模糊子集的基础上,给出更一般化的具有模糊支付与模糊赢得的两人零和模糊对策的模糊规划模型。利用模糊数的序方法,得到了此对策求解问题可以转化为带有模糊参数的两个经典规划的求解问题。文末给出算例予以说明。 相似文献
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4.
定义一般化两人零和模糊对策,分别对具有纯策略和混合策略的一般化两人零和模糊对策进行研究,得到相应的最小最大值定理,以及一些与经典矩阵对策相类似的结果。 相似文献
5.
Systems that involve more than one decision maker are often optimized using the theory of games. In the traditional game theory, it is assumed that each player has a well-defined quantitative utility function over a set of the player decision space. Each player attempts to maximize/minimize his/her own expected utility and each is assumed to know the extensive game in full. At present, it cannot be claimed that the first assumption has been shown to be true in a wide variety of situations involving complex problems in economics, engineering, social and political sciences due to the difficulty inherent in defining an adequate utility function for each player in these types of problems. On the other hand, in many of such complex problems, each player has a heuristic knowledge of the desires of the other players and a heuristic knowledge of the control choices that they will make in order to meet their ends.In this paper, we utilize fuzzy set theory in order to incorporate the players' heuristic knowledge of decision making into the framework of conventional game theory or ordinal game theory. We define a new approach to N-person static fuzzy noncooperative games and develop a solution concept such as Nash for these types of games. We show that this general formulation of fuzzy noncooperative games can be applied to solve multidecision-making problems where no objective function is specified. The computational procedure is illustrated via application to a multiagent optimization problem dealing with the design and operation of future military operations. 相似文献
6.
具有权限结构的合作对策可刻画合作者之间具有等级限制的情形,而具有模糊权限结构的合作对策是对经典情形的拓广.进一步考虑具有模糊权限结构和模糊支付的合作对策,利用联盟的自主度算子和模糊Choquet积分,定义了这种合作对策的限制对策.在此基础上给出了两种模糊权限值,分别证明了这两种值满足的一些性质.最后利用一个算例说明这两种值在企业协作生产收益分配中的应用. 相似文献
7.
一种n人静态博弈纯策略纳什均衡存在性判别法 总被引:6,自引:0,他引:6
本首先给出了n人静态博弈纯策略纳什均衡存在的充要条件。然后给出n人静态博弈纯策略纳什均衡存在性的一种判别方法。最后在判别纯策略纳什均衡存在的条件下,给出判定该静态博弈存在多少纯策略纳什均衡以及哪些纯策略组合是纯策略纳什均衡(解)的方法。 相似文献
8.
双人静态博弈纯战略纳什均衡存在性判别 总被引:3,自引:0,他引:3
李正龙 《应用数学与计算数学学报》2001,15(1):45-50
本文给出了双人有限静态博弈纯战略纳什均衡存在性的一种判别方法。并且,在纳什均衡存在的条件下,本判别法将给出纳什均衡解及解的唯一性判别。 相似文献
9.
We study a selection method for a Nash feedback equilibrium of a one-dimensional linear-quadratic nonzero-sum game over an infinite horizon. By introducing a change in the time variable, one obtains an associated game over a finite horizon T > 0 and with free terminal state. This associated game admits a unique solution which converges to a particular Nash feedback equilibrium of the original problem as the horizon T goes to infinity. 相似文献
10.
In this paper we consider the Nash equilibrium problem for infinite player games with vector payoffs in a topological vector
space setting. By employing new concepts of relative (pseudo)monotonicity, we establish several existence results of solutions
for usual and normalized vector equilibria. The results strengthen existence results for vector equilibrium problems, which
were based on classical pseudomonotonicity concepts. They also extend previous results for vector variational inequalities
and finite player games under relative (pseudo)monotonicity. 相似文献
11.
超级模数博弈的存在性 总被引:2,自引:0,他引:2
本文定义了一类在有序Banach空间上的超模博弈,并利用著名的Birkhoff不动点定理证明了有序Banach空间上超模博弈Nash均衡的存在性. 相似文献
12.
《佛山科学技术学院》2014,6(2):167-192
A recent research work of Clemente et al. [12] on Pareto-optimal security strategies (POSS) in matrix games with fuzzy payoffs is extended to I-fuzzy scenario. Besides, the membership and the non-membership functions of the I-fuzzy values for both players are obtained by employing the technique of multiobjective optimization. The presented approach provides an efficient solution to a class of I-fuzzy matrix games with piecewise linear membership and non-membership functions. This class also includes I-fuzzy matrix games with triangular and trapezoidal I-fuzzy numbers as special cases. Further, POSS approach also provides an approximate solution to I-fuzzy matrix games with payoffs as general I-fuzzy numbers. 相似文献
13.
The Nash equilibrium in pure strategies represents an important solution concept in nonzero sum matrix games. Existence of
Nash equilibria in games with known and with randomly selected payoff entries have been studied extensively. In many real
games, however, a player may know his own payoff entries but not the payoff entries of the other player. In this paper, we
consider nonzero sum matrix games where the payoff entries of one player are known, but the payoff entries of the other player
are assumed to be randomly selected. We are interested in determining the probabilities of existence of pure Nash equilibria
in such games. We characterize these probabilities by first determining the finite space of ordinal matrix games that corresponds
to the infinite space of matrix games with random entries for only one player. We then partition this space into mutually
exclusive spaces that correspond to games with no Nash equilibria and with r Nash equilibria. In order to effectively compute the sizes of these spaces, we introduce the concept of top-rated preferences
minimal ordinal games. We then present a theorem which provides a mechanism for computing the number of games in each of these
mutually exclusive spaces, which then can be used to determine the probabilities. Finally, we summarize the results by deriving
the probabilities of existence of unique, nonunique, and no Nash equilibria, and we present an illustrative example. 相似文献
14.
Wojciech Połowczuk Piotr Więcek Tadeusz Radzik 《Mathematical Methods of Operations Research》2007,65(1):141-152
This paper gives wide characterization of n-person non-coalitional games with finite players’ strategy spaces and payoff functions having some concavity or convexity
properties. The characterization is done in terms of the existence of two-point-strategy Nash equilibria, that is equilibria
consisting only of mixed strategies with supports being one or two-point sets of players’ pure strategy spaces. The structure
of such simple equilibria is discussed in different cases. The results obtained in the paper can be seen as a discrete counterpart
of Glicksberg’s theorem and other known results about the existence of pure (or “almost pure”) Nash equilibria in continuous
concave (convex) games with compact convex spaces of players’ pure strategies. 相似文献
15.
Kian A.R. Cruz J.B. Simaan M. A. 《Journal of Optimization Theory and Applications》2002,114(1):171-188
In this paper, we consider stochastic linear-quadratic discrete-time Nash games in which two players have access only to noise-corrupted output measurements. We assume that each player is constrained to use a linear Kalman filter-like state estimator to implement his optimal strategies. Two information structures available to the players in their state estimators are investigated. The first has access to one-step delayed output and a one-step delayed control input of the player. The second has access to the current output and a one-step delayed control input of the player. In both cases, statistics of the process and statistics of the measurements of each player are known to both players. A simple example of a two-zone energy trading system is considered to illustrate the developed Nash strategies. In this example, the Nash strategies are calculated for the two cases of unlimited and limited transmission capacity constraints. 相似文献
16.
Rincón-Zapatero J.P. Martín-Herrán G. 《Journal of Optimization Theory and Applications》2003,119(2):395-405
In this note, we present a method that allows us to decide when a Markov-perfect Nash equilibrium is not Pareto optimum, without the explicit knowledge of the respective solutions. For that purpose, we establish a sufficient condition in terms of an algebraic inequality where the gradient of the value functions of the cooperative and noncooperative games as well as the state and control variables are involved. 相似文献
17.
This paper studies two problems that arise in distributed computing. We deal with these problems from a game theoretical approach. We are interested in the convergence to the Nash equilibrium of algorithms based on the best reply strategy in a special case of linear costs. We present three specific types of algorithm that converge to the equilibrium. In our first model, composed of two processors, the convergence is established through monotonicity of the sequence of updates generated by each of the three algorithms. In the second model, made up of N processors, the convergence is due to the contraction of the algorithms. 相似文献
18.
On Coincidence of Feedback Nash Equilibria and Stackelberg Equilibria in Economic Applications of Differential Games 总被引:1,自引:0,他引:1
S. J. Rubio 《Journal of Optimization Theory and Applications》2006,128(1):203-220
The scope of the applicability of the feedback Stackelberg equilibrium concept in differential games is investigated. First,
conditions for obtaining the coincidence between the stationary feedback Nash equilibrium and the stationary feedback Stackelberg
equilibrium are given in terms of the instantaneous payoff functions of the players and the state equations of the game. Second,
a class of differential games representing the underlying structure of a good number of economic applications of differential
games is defined; for this class of differential games, it is shown that the stationary feedback Stackelberg equilibrium coincides
with the stationary feedback Nash equilibrium. The conclusion is that the feedback Stackelberg solution is generally not useful
to investigate leadership in the framework of a differential game, at least for a good number of economic applications
This paper was presented at the 8th Viennese Workshop on Optimal Control, Dynamic Games, and Nonlinear Dynamics: Theory and
Applications in Economics and OR/MS, Vienna, Austria, May 14–16, 2003, at the Seminar of the Instituto Complutense de Analisis
Economico, Madrid, Spain, June 20, 2003, and at the Sevilla Workshop on Dynamic Economics and the Environment, Sevilla, Spain,
July 2–3, 2003. The author is grateful to the participants in these sessions, in particular F.J. Andre and J. Ruiz, for their
comments. Five referees provided particularly helpful suggestions. Financial support from the Ministerio de Ciencia y Tecnologia
under Grant BEC2000-1432 is gratefully acknowledged. 相似文献
19.
运用广义最大元方法在非传递性偏好下给出了博弈均衡的存在性定理,推广了一些经典的博弈均衡存在性定理.在文中介绍策略式博弈的Nash均衡具有宽泛的条件,在微观经济理论中有广泛的应用. 相似文献
20.
In this paper, sufficient conditions are given, which are less restrictivethan those required by the Arrow–Debreu–Nash theorem, on theexistence of a Nash equilibrium of an n-player game {1, . . . , Yn,f1, . . . , fn} in normal form with a nonempty closedconvex constraint C on the set Y=i Yi of multistrategies. Theith player has to minimize the function fi with respect to the ithvariable. We consider two cases.In the first case, Y is a real Hilbert space and the loss function class isquadratic. In this case, the existence of a Nash equilibrium is guaranteedas a simple consequence of the projection theorem for Hilbert spaces. In thesecond case, Y is a Euclidean space, the loss functions are continuous, andfi is convex with respect to the ith variable. In this case, the techniqueis quite particular, because the constrained game is approximated with asequence of free games, each with a Nash equilibrium in an appropriatecompact space X. Since X is compact, there exists a subsequence of theseNash equilibrium points which is convergent in the norm. If thelimit point is in C and if the order of convergence is greater than one,then this is a Nash equilibrium of the constrained game. 相似文献