共查询到20条相似文献,搜索用时 15 毫秒
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A dynamic solution concept for abstract games 总被引:1,自引:0,他引:1
P. P. Shenoy 《Journal of Optimization Theory and Applications》1980,32(2):151-169
Several solution concepts have been defined for abstract games. Some of these are the core, due to Gillies and Shapley, the Von Neumann-Morgenstern stable sets, and the subsolutions due to Roth. These solution concepts are rather static in nature. In this paper, we propose a new solution concept for abstract games, called the dynamic solution, that reflects the dynamic aspects of negotiation among the players. Some properties of the dynamic solution are studied. Also, the dynamic solution of abstract games arising fromn-person cooperative games in characteristic function form is investigated.This research was supported by the Office of Naval Research under Contract No. N00014-75-C-0678, by the National Science Foundation under Grants Nos. MPS-75-02024 and MCS-77-03984 at Cornell University, by the United States Army under Contract No. DAAG-29-75-C-0024, and by the National Science Foundation under Grant No. MCS-75-17385-A01 at the University of Wisconsin. The author is grateful to Professor W. F. Lucas under whose guidance the research was conducted. 相似文献
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We formulate a cooperative game as an extended form game in which each player in turn proposes payoffs to a coalition over M steps. Payoffs at time t are discounted by a penalty function f(t). If all players in a coalition agree to their payoffs, they receive them. Under a convergence hypothesis verified by computer for three players in many cases, we compute the payoffs resulting from a coalition pattern and give necessary conditions for particular patterns. The resulting solution is related to the Nash bargaining solution and the competitive solution. 相似文献
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In this paper, sufficient criteria are established for the existence of periodic solutions of some functional dynamic equations with infinite delays on time scales, which generalize and incorporate as special cases many known results for differential equations and for difference equations when the time scale is the set of the real numbers or the integers, respectively. The approach is mainly based on the Krasnosel’ski? fixed point theorem, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in studying dynamic equations on time scales. This study shows that one can unify such existence studies in the sense of dynamic equations on general time scales. 相似文献
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This paper deals with the boundedness of the solutions of the following dynamic equations(r(t)x△(t))△+a(t)f(xσ(t))+b(t)g(xσ(t))=0and(r(t)x△(t))△+a(t)xσ(t)+b(t)f(x(t-τ(t)))=e(t)on a time scale T.By using the Bellman integral inequality,we establish some suffcient conditions for boundedness of solutions of the above equations.Our results not only unify the boundedness results for differential and difference equations but are also new for the q-difference equations. 相似文献
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《Applied Mathematical Modelling》2003,27(12):1035-1049
This article describes theoretical and experimental results on phase reflection diffraction gratings. Based on Fourier optics the mathematical formulation describing diffraction dispersion of light from a relief grating of the trapezium profile is derived. We propose a method that lets us estimate the grating’s geometric parameters in a versatile modelling system. We have designed an original programme that estimates diffraction intensities and calculates diffraction efficiency. The estimated intensities are used to reconstruct the grating’s geometrical properties using our mathematical model. The precision of the method is evaluated as the deviation of obtained results from microscopy data. 相似文献
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In this paper, we give an existence theorem for the extremal solutions for second order impulsive dynamic equations on time scales. 相似文献
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This paper is concerned with the existence and nonexistence of positive solutions of the second-order nonlinear dynamic equation uΔΔ(t)+λa(t)f(u(σ(t)))=0, t∈[0,1], satisfying either the conjugate boundary conditions u(0)=u(σ(1))=0 or the right focal boundary conditions u(0)=uΔ(σ(1))=0, where a and f are positive. We show that there exists a λ∗>0 such that the above boundary value problem has at least two, one and no positive solutions for 0<λ<λ∗, λ=λ∗ and λ>λ∗, respectively. Furthermore, by using the semiorder method on cones of the Banach space, we establish an existence and uniqueness criterion for positive solution of the problem. In particular, such a positive solution uλ(t) of the problem depends continuously on the parameter λ, i.e., uλ(t) is nondecreasing in λ, limλ→0+‖uλ‖=0 and limλ→+∞‖uλ‖=+∞. 相似文献
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L. Erbe A. Peterson Christopher C. Tisdell 《Nonlinear Analysis: Theory, Methods & Applications》2008,69(7):2303-2317
This paper focuses on the qualitative and quantitative properties of solutions to certain nonlinear dynamic equations on time scales. We present some new sufficient conditions under which these general equations admit a unique, positive solution. These positive (and hence non-oscillatory) solutions: extend across unbounded intervals; and tend to a finite limit as the independent variable becomes large and positive. Our methods include: Banach’s fixed-point theorem, including the method of Picard iterations; and weighted norms and metrics in the time scale setting. Due to the wide-ranging nature of dynamic equations on time scales our results are novel: for ordinary differential equations; for difference equations; for combinations of the two areas; and for general time scales — this is demonstrated via some examples. Furthermore, we state an open problem of interest. 相似文献
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A three-dimensional analytical solution describing forced harmonic vibrations of prestressed laminated plates is found for the case of a hinged support. The solution is based on the analytical separation of variables. It is assumed that the prestressed state is homogeneous, subcritical, linear, and momentless and that the vibration amplitudes are small. A solution based on a model with a polynomial approximation of the required displacement functions across the plate thickness is also considered. These functions are found on the front surfaces of the structure. This allows us to solve the problem both in the continuous and discrete structural approaches. In the continuous structural approach, the order of the resolving system of equations is independent of the number of layers. In the discrete structural approach, for rigid contact of layers with similar boundary conditions at the plate end face, an algorithm can be introduced which reduces significantly the number of operations required for realization of the model proposed. In the numerical examples presented, both rigid and sliding contacts of layers and various prestressed conditions are considered. Both approaches give results that agree well. 相似文献
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非线性耦合标量场方程显式解析解的研究 总被引:2,自引:0,他引:2
利用两种不同的变换,获得了一类非线性耦合标量场方程的若干类型的精确解析解,其中包括孤子解、奇性孤波解和三角函数解,从而丰富了方程解的内容。这些结论可以应用于其它的非线性方程。此外还纠正了一些文献的部分结论。 相似文献
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The weak formulation of parabolic problems with dynamic boundary conditions is rewritten in form of a partial differential–algebraic equation. More precisely, we consider two dynamic equations with a coupling condition on the boundary. This constraint is included explicitly as an additional equation and incorporated with the help of a Lagrange multiplier. Well-posedness of the formulation is shown. 相似文献
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《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):137-161
An optimal stochastic control problem is considered in this paper, where the diffusion coefficient also depends on the control and is possibly degenerate. In addition to the usual adjoint process, a second-order adjoint process is introduced. Some relationships between the value function and the adjoint processes are presented via the “super- and sub-differential” which is related to the viscosity solution, without assuming the smoothness of the value function. The maximum principle, dynamic programming and their connections are then established within a unified framework of viscosity solution 相似文献
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An inequality model for solving interval dynamic response of structures with uncertain-but-bounded parameters 总被引:1,自引:0,他引:1
In this paper, we look into the dynamic response of structures with uncertain-but-bounded parameters. A new inequality model for determining the interval dynamic response is presented. First we propose an interval dynamic response solution theorem. An inequality model which is a mathematics programming problem is suggested by the presented theorem. Using the central difference method, we substitute the differential items of the inequality model by difference items. By solving them, the interval dynamic response can be obtained. Two examples are used to illustrate the feasibility and the efficiency of the model. 相似文献