On the existence of a minimum integer representation for?weighted voting systems

A basic problem in the theory of simple games and other fields is to study whether a simple game (Boolean function) is weighted (linearly separable). A second related problem consists in studying whether a weighted game has a minimum integer realization. In this paper we simultaneously analyze both problems by using linear programming. For less than 9 voters, we find that there are 154 weighted games without minimum integer realization, but all of them have minimum normalized realization. Isbell in 1958 was the first to find a weighted game without a minimum normalized realization, he needed to consider 12 voters to construct a game with such a property. The main result of this work proves the existence of weighted games with this property with less than 12 voters. This research was partially supported by Grant MTM 2006-06064 of “Ministerio de Ciencia y Tecnología y el Fondo Europeo de Desarrollo Regional” and SGRC 2005-00651 of “Generalitat de Catalunya”, and by the Spanish “Ministerio de Ciencia y Tecnología” programmes ALINEX (TIN2005-05446 and TIN2006-11345).     

Zero-Sum Ergodic Semi-Markov Games with Weakly Continuous Transition Probabilities

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.     

Potential games and well-posedness properties

The aim of this article is to study potential games which are a special class of games, in fact their properties are dictated by a single function called the potential function. We consider Tikhonov well-posedness and other well-posedness properties introduced by the authors in Margiocco et al. (Margiocco, M., Patrone, F. and Pusillo Chicco, L., 1997, A new approach to Tikhonov well–posedness for Nash equilibria. Optimization, 40, 385–400) Margiocco and Pusillo (Margiocco, M. and Pusillo, L., Value bounded approximations for Nash equilibria, Preprint, Submitted). We relate these properties with the Tikhonov well posedness of the potential function as maximum problem.     

Semi-infinite programming,duality, discretization and optimality conditions†

The aim of this article is to give a survey of some basic theory of semi-infinite programming. In particular, we discuss various approaches to derivations of duality, discretization, and first- and second-order optimality conditions. Some of the surveyed results are well known while others seem to be less noticed in that area of research.     

An advertising game with multiplicative interference

Two competing manufacturers provide a homogeneous market with substitutable products and want to maximize their profits. Each firm may advertise its brand, with a positive effect on its own brand and negative on the competitor's one. Moreover, each firm may choose an advertising medium to use among several available media. We assume that the advertising effect on demand is mediated by the goodwill variable and that a competitor's interference may be represented as a proportional reduction of the virtual goodwill. We model the manufacturers' problem as a noncooperative game under complete information and discuss the existence and features of its Nash equilibria.     

Complexity of games and bounded rationality

An attempt is made to propose a concept of limited rationality for choice junctions based on computability theory in computer science.

Starting with the observation that it is possible to construct a machine simulating strategies of each individual in society, one machine for each individual's preference structure, we identify internal states of this machine with strategies or strategic preferences. Inputs are possible actions of other agents in society thus society is effectively operating as a game generated by machines. The main result states that effective realization of game strategies bound by the “complexity of computing machines'.     

Burgers方程的一类自相似解

利用李群理论中的伸缩变换群,将二阶非线性偏微分方程-Burgers方程化为一类Riccati方程和三类二阶非线性常微分方程,从而Riccati方程和这三类二阶非线性常微分方程给出了Burgers方程的自相似解的表现形式.     

动态需求背景下两阶段供应链博弈分析

在两阶段供应链中,市场营销也会导致需求的变动.引入营销费用与零售价格共同影响市场需求,并假设卖方决定订货批量,分别从非合作博弈和合作博弈两个角度对两阶段供应链管理问题进行分析.非合作博弈分析的是卖方或买方分别作为领导者时的Stackelberg模型;合作博弈是把卖方和买方的利润函数加权后作为目标函数,求出了帕累托最优解.结果证明,在合作博弈中存在帕累托有效解,与非合作博弈相比,合作博弈的订货批量更小,零售价格更低,市场营销费用更少.并列举案例,对模型中主要参数进行敏感性分析.     

具有模糊权限结构和模糊支付的合作对策

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.