How Hierarchical Structures Impact on Competition

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.Hierarchical structures, multi-level Stackelberg equilibrium, Nash-Cournot equilibrium

Optimal Scanning Bandwidth Strategy Incorporating Uncertainty about Adversary's Characteristics

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.Comment: This is the last draft version of the paper. Revised version of the paper was published in EAI Endorsed Transactions on Mobile Communications and Applications, Vol. 14, Issue 5, 2014, doi=10.4108/mca.2.5.e6. arXiv admin note: substantial text overlap with arXiv:1310.724

Fish Wars: Cooperative and Non-Cooperative Approaches

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.Nash equilibrium, multistage game, fish war game, cooperative behavior

Multilevel Pricing Schemes in a Deregulated Wireless Network Market

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.Comment: This is the last draft version of the paper. Revised version of the paper accepted by ValueTools 2013 can be found in Proceedings of the 7th International Conference on Performance Evaluation Methodologies and Tools (ValueTools '13), December 10-12, 2013, Turin, Ital

Closed form solutions for symmetric water filling games

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

Long-Term Energy Constraints and Power Control in Cognitive Radio Networks

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.Comment: DSP 2011: 17th International Conference on Digital Signal Processing, July 2011, Corfu, Greec

Closed form solutions for symmetric water filling games

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

Optimal hierarchical pricing schemes for wireless network usage and resource allocation

Session 06 : Network neutrality and regulationInternational audienceTypically the cost of a product has many components. Various components correspond to the production chain steps through which the product goes before meeting a customer. This also takes place in the price formation in wireless networks. For instance, before transmitting customer data, a network operator has to buy some frequency range and also establish contracts with electricity providers. In this paper we try to establish the tariff formation scheme in wireless networks. We consider an hierarchical game with three levels: the user, the provider and the authority. The user intends to transmit data on a network. The amount of traffic sent by the user depends on the available frequency bandwidth as well as on the tariff. The amount of frequency bandwidth is negotiated between the provider and the authority. A natural question arises for the provider: which tariff the provider has to assign to get the maximal pure profit, i.e. different between how much he obtains from the user and how much he has to pay for the reserved frequency bandwidth to the authority. The authority also looks for the frequency bandwidth tariff which can bring a maximal profit for him. We consider a Stackelberg game model with three levels of hierarchy: the authority as the leader of the first level, the provider who is the follower for the authority and the leader for the lower level, and the user who is the follower for the provider. The formulas for optimal tariffs at each level are established and some very interesting properties of the equilibrium are investigated. The authority obtains more profit by reducing the bandwidth frequency tariff, meanwhile the provider achieves better profit by increasing the user's rate tariff. In fact, our mathematical model can confirm the opinion that the telecom companies have payed too much for 3G licences. Finally, we note that the main novelty in this paper compared to the standard Stackelberg pricing games extensively investigated in the literature is that we consider the three level hierarchical structure user-provider-authority

Taxation for Green Communication

Game-Theoretic Models and SecurityInternational audienceNowadays energy saving and reduction of electromagnetic pollution become important issues. One approach to these problems is the introduction of taxes on the energy dissipation. In this paper we investigate a taxation game between a user or a provider or a group of users and the taxation authority. This is a Stackelberg game where the taxation authority acts as a leader and users or service providers act as followers. Clearly too big taxes will strongly discourage the user of wireless technology and hinder the progress and too small taxes will lead to a wasteful use of the energy resources and may also lead to reckless use of the radio resources. We study several important particular cases with complete and partial information. We focus on the problem of finding taxation strategy in closed form and investigating how incomplete information of authorities about users impacts the equilibrium strategy

A Bayesian Jamming Game in an OFDM Wireless Network

Games and LearningInternational audienceThe goal of this paper is to investigate how incomplete information on the fading channel gains impacts transmission parameters. We consider in an OFDM network with transmitters and jammers. To deal with this situation we employ a Bayesian approach by introducing different type of user and jammer corresponding to their knowledge of the network environment. To get an insight of the problem, the signal to interference and noise ratio (SINR) is considered as the main metric to optimize. First, equilibrium are found in closed form expressions. Second, we show interesting results saying that incomplete information on the jammer channel gains leads to equilibrium strategies which correspond to utilization of the same channels by the different types of the jammer. Meanwhile incomplete information about the transmitter leads to channels sharing transmission equilibrium strategies employed by different types of users