Dynamic Strategic Pricing and Speed of Diffusion

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.     

The rule of affine similitude for the force coefficients of a body oscillating in a uniformly stratified fluid

 This paper presents a study on affine similitude for the force coefficients of an arbitrary body oscillating in a uniformly stratified fluid. A simple formula is derived that gives a relation between the force coefficients for a body oscillating in homogeneous and uniformly stratified ideal fluids. In particular, it implies the existence of a universal nondimensional similitude criterion for a family of affinely similar bodies, namely, the bodies that can be transformed into each other by vertical dilation of the initial coordinate system. Theoretical results are verified by experiments with a set of spheroids having different length-to-diameter ratios. The experimental technique for evaluation of the frequency-dependent force coefficients is based on Fourier analysis of the time-history of damped oscillation tests. Received: 25 September 2000 / Accepted: 6 July 2001 Published online: 29 November 2001     

New Kamenev-type oscillation criteria for second-order nonlinear differential equations with damping

Some new oscillation criteria are established for the nonlinear damped differential equation (r(t)y′)′+p(t)y′+q(t)f(y)=0 that are different from most known ones in the sense that they are based on a class of new functions Φ(t,s,r) defined in the sequel. Our results are sharper than some previous results which can be seen by the examples at the end of this paper.     

Action learning versus strategy learning

This article seeks to ascertain whether the strategy‐learning model of Hanaki, Sethi, Erev, and Peterhansl (2003) better accounts for observed behavior than do the various action‐learning models. It does so by measuring the goodness‐of‐fit of the models' predictions against published experimental results for such games as Coordination, Prisoner's Dilemma, and Chicken. The fit is measured via the mean squared deviation (MSD) between the observed behavior and the one predicted by the model. The results show that, for Chicken, the strategy‐learning model fits the observed data much better than do the action‐learning models. The best action‐learning model, on the other hand, fits the observed data well in Coordination. Overall, the strength of the strategy‐learning model is best shown in games where alternations between the two stage‐game Nash equilibria are often observed in the laboratory experiments. © 2004 Wiley Periodicals, Inc. Complexity 9: 41–50, 2004     

Noninferior Nash Strategies for Multi-Team Systems

This paper is concerned with the optimization of systems that are controlled by several teams of decision makers. The decision makers within each team cooperate for the benefit of their team. On the other hand, the teams compete among themselves in order to achieve an objective that relates to the overall performance of the system. An approach that merges concepts from team theory and game theory for dealing with such systems and a solution called the noninferior Nash strategy are introduced. This multi-team solution provides a new framework for analyzing hierarchically controlled systems so as to address complicated coordination problems among the decision makers. The properties of the noninferior Nash solution in static multi-team systems are investigated and necessary conditions for its existence are derived. Analytical expressions for the noninferior Nash strategies are derived for a class of linear-quadratic static multi-team games. In order to deal with the issue of nonuniqueness of the solution, the concept of a noninferior Nash strategy with a team leader is introduced. Several examples are presented to illustrate the results.     

基于指数分布的进化策略

典型的进化策略受自然进化过程的启发而成为求解全局优化问题的重要方法。传统的ES变异算子作为一个主要的进化技术是建立在正态分布的随机变量基础上的，本文提出了基于指数分布的进化策略由于采用了新的变异算子有效地减少了产生探试解的成本，从而优于传统的进化策略。     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Stabilizing an uncertain production system

Consider a production system that consists ofm machines each of which can produce parts ofn types. When machinek is used, it produces a part of typei with probabilityp _ki . Requests arrive for parts, one at a time. With probability _i an arriving request is for a part of typei. The requests must be served without waiting. Thus, if a requested part is not available, it must be produced. We find necessary and sufficient conditions for the existence of a strategy (a choice of the machines to be used) which makes the inventory of parts stable and we provide such a strategy.Two variations of this model are also considered: the case of batch arrivals of requests, and that of a system where the requests can be queued.     

Tactical problems involving uncertain actions

The purpose of this paper is to solve anm-silent versusn-silent duel with arbitrary accuracy functionsP andQ which are continuously differentiable in [0, 1] with positive derivatives in (0, 1) and such thatP(0)=Q(0)=0,P(1)(0, 1),Q(1)(0, 1). The game can be interpreted as a game in which the players know only that the numbers of their actions have binomial distribution.Part of this paper was written during the author's stay at the Institute of Statistics and Mathematical Economics, University of Karlsruhe, FRG. The author wishes to thank Prof. S. Trybua, Technical University of Wrocaw, Poland, for helpful discussion in preparing the paper and Prof. D. Pallaschke, University of Karlsruhe, FRG, for help in preparing the numerical example.