基于模糊数的政府与绿色制造商博弈分析

近年来环境问题已经成为人们迫切需要解决的重要问题,促使制造商采取绿色制造模式也是各国政府正在面临的一大难题。因此文章结合三角模糊数与博弈理论建立了政府与绿色制造商的模糊博弈模型,将博弈结果分为纯策略和混合策略两类,并讨论了各种情形下政府与绿色制造商的不同策略以及影响因素,分析了最优博弈结果以及相应的管理策略,为绿色制造模式的顺利实施提供了相关建议。研究结果表明,政府的补贴和惩罚等策略在绿色制造模式的采取方面起着举足轻重的作用。最后利用三角结构元法对算例分纯策略和混合策略两种情况进行分析求解,从而验证了结论的正确性和可行性。     

Accumulation Games,Part 1: Noisy Search

In an accumulation game, a hider places objects at locations, and a seeker examines these locations. If the seeker discovers an object, the seeker confiscates it. The goal of the hider is to accumulate a certain number of objects before a given time, and the goal of the seeker is to prevent this. In this paper, we first classify various possible variations on the accumulation game. Next, we discuss the so-called noisy accumulation game in which the hider can observe each action of the seeker. We present the solution of this game for all but some marginal cases and illustrate it with computational examples.     

宏观调控政策协调的TU和NTU合作博弈分析

宏观经济政策之间的协调及其调控收益的分配实际上可看做n人合作博弈.通过构造宏观政策组合的二人TU博弈模型,分析了政策组合的调控力度、收益及其分配比例值的相互关系,并重新构建政策组合调控总收益的特征函数,把宏观政策协调的二人TU博弈分析依次扩展至n人TU博弈情形和NTU博弈情形,给出相应的政策调控收益分配的Shapley值,提出确定宏观政策组合中各项政策调控的参与力度的具体办法,有效地解释了加强政策协调配合的宏观调控精神,对宏观调控实践具有一定的指导意义.     

A Degree Sum Condition Concerning the Connectivity and the Independence Number of a Graph

Let G be a graph and S ⊂ V(G). We denote by α(S) the maximum number of pairwise nonadjacent vertices in S. For x, y ∈ V(G), the local connectivity κ(x, y) is defined to be the maximum number of internally-disjoint paths connecting x and y in G. We define . In this paper, we show that if κ(S) ≥ 3 and for every independent set {x ₁, x ₂, x ₃, x ₄} ⊂ S, then G contains a cycle passing through S. This degree condition is sharp and this gives a new degree sum condition for a 3-connected graph to be hamiltonian.     

Search and Ambush Games with Capacities

Search games with capacities are bipersonal zero-sum games where a player has to hide a number of objects or an amount of material in a fixed number of containers and his opponent attempts to locate them. In this article, we deal with games on a discrete structureless set and on a discrete set with linear order. In both cases, the capacities under consideration are continuous. Some of the games studied generalize previously studied games.     

带有尖形式Fourier系数的指数和估计

设λ_f/(n)是全模群Γ上权为k的全纯Hecke特征形f的第n个Fourier系数,Λ(n)是Mangoldt函数.本文得到了如下估计∑_(Xn≤2X)Λ(n)λ_f(n)e(n~(1/2)α)■f,αX~(5/6)(logX)~(13/2),(α0),改进了Zhao的结果。     

A Survey on Topological Properties of Tiles Related to Number Systems

In the present paper we give an overview of topological properties of self-affine tiles. After reviewing some basic results on self-affine tiles and their boundary we give criteria for their local connectivity and connectivity. Furthermore, we study the connectivity of the interior of a family of tiles associated to quadratic number systems and give results on their fundamental group. If a self-affine tile tessellates the space the structure of the set of its ‘neighbors’ is discussed.     

Continuous Accumulation Games in Continuous Regions

In a continuous accumulation game on a continuous region, a Hider distributes material over a continuous region at each instant of discrete time, and a Seeker examines the region. If the Seeker locates any of the material hidden, the Seeker confiscates it. The goal of the Hider is to accumulate a certain amount of material before a given time, and the goal of the Seeker is to prevent this. In previous works, we have studied accumulation games involving discrete objects and continuous material over discrete locations. The issues raised when the region is continuous are substantially different. In this paper, we study accumulation of continuous material over two types of continuous regions: the interval and the circle.     

二人零和连续对策上的判断与最优策略间的关系

引进了二人零和连续对策上的判断，判断块以及在判断下的最优策略等概念．研究了判断下的最优策略集与经典最优策略集之间的关系，得到了一些在理论上有趣而且有用的结果．     

On the subset sum problem for finite fields

Let G be the additive group of a finite field. J. Li and D. Wan determined the exact number of solutions of the subset sum problem over G, by giving an explicit formula for the number of subsets of G of prescribed size whose elements sum up to a given element of G. They also determined a closed-form expression for the case where the subsets are required to contain only nonzero elements. In this paper we give an alternative proof of the two formulas. Our argument is purely combinatorial, as in the original proof by Li and Wan, but follows a different and somehow more “natural” approach. We also indicate some new connections with coding theory and combinatorial designs.     

On the Number of Sparse RSA Exponents

An RSA modulus is a product M=pl of two primes p and l. We show that for almost all RSA moduli M, the number of sparse exponents e (which allow for fast RSA encryption) with the property that gcd(e,?(M))=1 (hence RSA decryption can also be performed) is very close to the expected value.     

Analysis of the N-Card Version of the Game Le Her

We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.     

A Differential R&D Game: Implications for Knowledge-Based Growth Models

This paper compares the outcomes of strategic and nonstrategic research and development (R&D). Firms undertake cost-reducing R&D in an environment where benefits accrue from their rivals' R&D via a common pool of knowledge. We demonstrate that multiple suboptimal equilibria exist; under these conditions, growth models which do not consider strategic interactions will overestimate or underestimate the growth rate.     

Selecting the Number of Knots for Penalized Splines

Penalized splines, or P-splines, are regression splines fit by least-squares with a roughness penalty.P-splines have much in common with smoothing splines, but the type of penalty used with a P-spline is somewhat more general than for a smoothing spline. Also, the number and location of the knots of a P-spline is not fixed as with a smoothing spline. Generally, the knots of a P-spline are at fixed quantiles of the independent variable and the only tuning parameters to choose are the number of knots and the penalty parameter. In this article, the effects of the number of knots on the performance of P-splines are studied. Two algorithms are proposed for the automatic selection of the number of knots. The myopic algorithm stops when no improvement in the generalized cross-validation statistic (GCV) is noticed with the last increase in the number of knots. The full search examines all candidates in a fixed sequence of possible numbers of knots and chooses the candidate that minimizes GCV.The myopic algorithm works well in many cases but can stop prematurely. The full-search algorithm worked well in all examples examined. A Demmler–Reinsch type diagonalization for computing univariate and additive P-splines is described. The Demmler–Reinsch basis is not effective for smoothing splines because smoothing splines have too many knots. For P-splines, however, the Demmler–Reinsch basis is very useful for super-fast generalized cross-validation.     

On Explicit Formulas for the Number of Solutions to the Equation (x1+...+xn)2 =ax1...xn in a Finite Field

We consider the equation of the title in a finite field of q elements. Assuming certain relations between n and q, we obtain explicit formulas for the number of solutions to this equation.     

关于幂和公式系数的一个递推关系式

本文给出幂和公式中的系数的一个递推关系式 ,并且还得到直接计算系数及把系数表为因式乘积的两个推论 .     

Enumeration of All the Extreme Equilibria in Game Theory: Bimatrix and Polymatrix Games

Bimatrix and polymatrix games are expressed as parametric linear 0–1 programs. This leads to an algorithm for the complete enumeration of their extreme equilibria, which is the first one proposed for polymatrix games. The algorithm computational experience is reported for two and three players on randomly generated games for sizes up to 14 × 14 and 13 × 13 × 13.Communicated by P. M. PardalosThe authors thank Bernhard von Stengel for constructive comments on the contents of this paper.     

A class of trilinear differential games

This paper characterizes a class ofN-person, general sum differential games for which the optimal strategies only depend upon remaining playing time. Such strategies can be easily characterized and determined, and the optimal play can be easily analyzed.We acknowledge the helpful comments of G. Leitmann and an anonymous referee.     

合作博弈视角分析社会财富分配

对具有超可加性质的绩效博弈中几种不同“核”分配方案进行研究,利用数学方法证明了这些“核”分配方案之间的包含关系.管理者们可以利用这种包含关系对分配方案进行改进,来寻找最稳定的“核”分配方案.并提出了一些分配方案改进的建议.