Evolutionary Poisson Games for Controlling Large Population Behaviors

Emerging applications in engineering such as crowd-sourcing and (mis)information propagation involve a large population of heterogeneous users or agents in a complex network who strategically make dynamic decisions. In this work, we establish an evolutionary Poisson game framework to capture the random, dynamic and heterogeneous interactions of agents in a holistic fashion, and design mechanisms to control their behaviors to achieve a system-wide objective. We use the antivirus protection challenge in cyber security to motivate the framework, where each user in the network can choose whether or not to adopt the software. We introduce the notion of evolutionary Poisson stable equilibrium for the game, and show its existence and uniqueness. Online algorithms are developed using the techniques of stochastic approximation coupled with the population dynamics, and they are shown to converge to the optimal solution of the controller problem. Numerical examples are used to illustrate and corroborate our results

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

Spectrum Coordination in Energy Efficient Cognitive Radio Networks

Device coordination in open spectrum systems is a challenging problem, particularly since users experience varying spectrum availability over time and location. In this paper, we propose a game theoretical approach that allows cognitive radio pairs, namely the primary user (PU) and the secondary user (SU), to update their transmission powers and frequencies simultaneously. Specifically, we address a Stackelberg game model in which individual users attempt to hierarchically access to the wireless spectrum while maximizing their energy efficiency. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium is conducted. In particular, we show that a spectrum coordination naturally occurs when both actors in the system decide sequentially about their powers and their transmitting carriers. As a result, spectrum sensing in such a situation turns out to be a simple detection of the presence/absence of a transmission on each sub-band. We also show that when users experience very different channel gains on their two carriers, they may choose to transmit on the same carrier at the Stackelberg equilibrium as this contributes enough energy efficiency to outweigh the interference degradation caused by the mutual transmission. Then, we provide an algorithmic analysis on how the PU and the SU can reach such a spectrum coordination using an appropriate learning process. We validate our results through extensive simulations and compare the proposed algorithm to some typical scenarios including the non-cooperative case and the throughput-based-utility systems. Typically, it is shown that the proposed Stackelberg decision approach optimizes the energy efficiency while still maximizing the throughput at the equilibrium.Comment: 12 pages, 10 figures, to appear in IEEE Transactions on Vehicular Technolog

On the Two-user Multi-carrier Joint Channel Selection and Power Control Game

In this paper, we propose a hierarchical game approach to model the energy efficiency maximization problem where transmitters individually choose their channel assignment and power control. We conduct a thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium. Interestingly, we formally show that a spectrum orthogonalization naturally occurs when users decide sequentially about their transmitting carriers and powers, delivering a binary channel assignment. Both analytical and simulation results are provided for assessing and improving the performances in terms of energy efficiency and spectrum utilization between the simultaneous-move game (with synchronous decision makers), the social welfare (in a centralized manner) and the proposed Stackelberg (hierarchical) game. For the first time, we provide tight closed-form bounds on the spectral efficiency of such a model, including correlation across carriers and users. We show that the spectrum orthogonalization capability induced by the proposed hierarchical game model enables the wireless network to achieve the spectral efficiency improvement while still enjoying a high energy efficiency.Comment: 31 pages, 13 figures, accepted in IEEE Transactions on Communication

A Game Theoretic Analysis for Energy Efficient Heterogeneous Networks

Smooth and green future extension/scalability (e.g., from sparse to dense, from small-area dense to large-area dense, or from normal-dense to super-dense) is an important issue in heterogeneous networks. In this paper, we study energy efficiency of heterogeneous networks for both sparse and dense two-tier small cell deployments. We formulate the problem as a hierarchical (Stackelberg) game in which the macro cell is the leader whereas the small cell is the follower. Both players want to strategically decide on their power allocation policies in order to maximize the energy efficiency of their registered users. A backward induction method has been used to obtain a closed-form expression of the Stackelberg equilibrium. It is shown that the energy efficiency is maximized when only one sub-band is exploited for the players of the game depending on their fading channel gains. Simulation results are presented to show the effectiveness of the proposed scheme.Comment: 7 pages, 3 figures, in Wiopt 201