Abstract:
Stackelberg models for hierarchical oligopolistic markets with a homogenous product were studied by researchers extensively. The goal of this paper is to extend the classical solution in closed form of the Stackelberg model for a general hierarchical structures composed by firms arranged into groups of different hierarchical levels.

Abstract:
Mirman (1979) and Levhari and Mirman (1980) suggested a simple two person multistage game-theoretical model which sheds some light on the economic implications inherent in the fishing conflicts where the decisions of the competitors have an effect on the evolution of the fish population and so, on the future expected profit of the competitors. In this paper we consider a generalization of the Levhari and Mirman Fish War Game for the case of n participants of the conflict for different scenarios of hierarchical and coalition structures of countries. We derive the equilibrium and its steady-state behavior for all these scenarios and analyze the impact which the hierarchical and coalition structures can have on fishery and ecology.

Abstract:
In this paper we investigate the problem of designing a spectrum scanning strategy to detect an intelligent Invader who wants to utilize spectrum undetected for his/her unapproved purposes. To deal with this problem we model the situation as two games, between a Scanner and an Invader, and solve them sequentially. The first game is formulated to design the optimal (in maxmin sense) scanning algorithm, while the second one allows one to find the optimal values of the parameters for the algorithm depending on parameters of the network. These games provide solutions for two dilemmas that the rivals face. The Invader's dilemma consists of the following: the more bandwidth the Invader attempts to use leads to a larger payoff if he is not detected, but at the same time also increases the probability of being detected and thus fined. Similarly, the Scanner faces a dilemma: the wider the bandwidth scanned, the higher the probability of detecting the Invader, but at the expense of increasing the cost of building the scanning system. The equilibrium strategies are found explicitly and reveal interesting properties. In particular, we have found a discontinuous dependence of the equilibrium strategies on the network parameters, fine and the type of the Invader's award. This discontinuity of the fine means that the network provider has to take into account a human/social factor since some threshold values of fine could be very sensible for the Invader, while in other situations simply increasing the fine has minimal deterrence impact. Also we show how incomplete information about the Invader's technical characteristics and reward (e.g. motivated by using different type of application, say, video-streaming or downloading files) can be incorporated into scanning strategy to increase its efficiency.

Abstract:
We study power control in optimization and game frameworks. In the optimization framework there is a single decision maker who assigns network resources and in the game framework users share the network resources according to Nash equilibrium. The solution of these problems is based on so-called water-filling technique, which in turn uses bisection method for solution of non-linear equations for Lagrange multiplies. Here we provide a closed form solution to the water-filling problem, which allows us to solve it in a finite number of operations. Also, we produce a closed form solution for the Nash equilibrium in symmetric Gaussian interference game with an arbitrary number of users. Even though the game is symmetric, there is an intrinsic hierarchical structure induced by the quantity of the resources available to the users. We use this hierarchical structure to perform a successive reduction of the game. In addition, to its mathematical beauty, the explicit solution allows one to study limiting cases when the crosstalk coefficient is either small or large. We provide an alternative simple proof of the convergence of the Iterative Water Filling Algorithm. Furthermore, it turns out that the convergence of Iterative Water Filling Algorithm slows down when the crosstalk coefficient is large. Using the closed form solution, we can avoid this problem. Finally, we compare the non-cooperative approach with the cooperative approach and show that the non-cooperative approach results in a more fair resource distribution.

Abstract:
Typically the cost of a product, a good or a service has many components. Those components come from different complex steps in the supply chain of the product from sourcing to distribution. This economic point of view also takes place in the determination of goods and services in wireless networks. Indeed, before transmitting customer data, a network operator has to lease some frequency range from a spectrum owner and also has to establish agreements with electricity suppliers. The goal of this paper is to compare two pricing schemes, namely a power-based and a flat rate, and give a possible explanation why flat rate pricing schemes are more common than power based pricing ones in a deregulated wireless market. We suggest a hierarchical game-theoretical model of a three level supply chain: the end users, the service provider and the spectrum owner. The end users intend to transmit data on a wireless network. The amount of traffic sent by the end users depends on the available frequency bandwidth as well as the price they have to pay for their transmission. A natural question arises for the service provider: how to design an efficient pricing scheme in order to maximize his profit. Moreover he has to take into account the lease charge he has to pay to the spectrum owner and how many frequency bandwidth to rent. The spectrum owner itself also looks for maximizing its profit and has to determine the lease price to the service provider. The equilibrium at each level of our supply chain model are established and several properties are investigated. In particular, in the case of a power-based pricing scheme, the service provider and the spectrum owner tend to share the gross provider profit. Whereas, considering the flat rate pricing scheme, if the end users are going to exploit the network intensively, then the tariffs of the suppliers (spectrum owner and service provider) explode.

Abstract:
When a long-term energy constraint is imposed to a transmitter, the average energy-efficiency of a transmitter is, in general, not maximized by always transmitting. In a cognitive radio context, this means that a secondary link can re-exploit the non-used time-slots. In the case where the secondary link is imposed to generate no interference on the primary link, a relevant issue is therefore to know the fraction of time-slots available to the secondary transmitter, depending on the system parameters. On the other hand, if the secondary transmitter is modeled as a selfish and free player choosing its power control policy to maximize its average energy-efficiency, resulting primary and secondary signals are not necessarily orthogonal and studying the corresponding Stackelberg game is relevant to know the outcome of this interactive situation in terms of power control policies.

Abstract:
In this paper we investigate the problem of designing a spectrum scanning strategy to detect an intelligent Invader who wants to utilize spectrum undetected for his/her unapproved purposes. To deal with this problem we apply game-theoretical tools. We model the situation as a game between a Scanner and an Invader where the Invader faces a dilemma: the more bandwidth the Invader attempts to use leads to a larger payoff if he is not detected, but at the same time also increases the probability of being detected and thus fined. Similarly, the Scanner faces a dilemma: the wider the bandwidth scanned, the higher the probability of detecting the Invader, but at the expense of increasing the cost of building the scanning system. The equilibrium strategies are found explicitly and reveal interesting properties. In particular, we have found a discontinuous dependence of the equilibrium strategies on the network parameters, fine and the type of the Invader's award. This discontinuity on fine means that the network provider has to take into account a human factor since some threshold values of fine could be very sensible for the Invader, while in other situations simply increasing the fine has minimal deterrence impact. Also we show how different reward types for the Invader (e.g. motivated by using different type of application, say, video-streaming or downloading files) can be incorporated into scanning strategy to increase its efficiency.

Abstract:
The
generation of an attosecond pulse in the ultraviolet range is described in the
terms of the catastrophe theory. A simple criterion of tunneling is proposed.
The criterion allows constructing the quasiclassical model of the generator of
attosecond laser pulses based on the interaction of an electric field of extremely
powerful femtosecond
pulse with the valence electron in the potential well of the gas atom.

Abstract:
In this paper, the superfluid substance is described by the same equations of the electromagnetic field and the gravitational field. The gravitational mass is sufficiently considered as the gravitational charge, having the same dimensions as electric charge.

Abstract:
In
today’s society, the rapid development of the knowledge-based economy puts
forward new requirements for the leadership of enterprises: improving the ideas
of employees and enterprises, improving leadership art has become extremely
important content for the leadership management model in this new era.
Leadership art is the content and performance of the leadership style. The
correct use of leadership art is very important for the whole enterprise. It
can not only effectively improve the efficiency of the enterprise, but also promote the common development of the company
and employees. However, how to make the successful use of leadership art
in enterprises has become an urgent problem to be solved. In this article, two
or more existing situations are studied to determine their similarities and
differences, the background, development, current conditions and environmental
interactions of one or more individuals, groups, communities, businesses or
institutions is observed, recorded and analyzed for stages of patterns in
relation to internal and external influences. This article will briefly discuss
the influence of leadership art on modern enterprise management.