In this paper, we tackle the problem of opportunistic spectrum access in large-scale cognitive radio networks, where the unlicensed Secondary Users (SU) access the frequency channels partially occupied by the licensed Primary Users (PU). Each channel is characterized by an availability probability unknown to the SUs. We apply evolutionary game theory to model the spectrum access problem and develop distributed spectrum access policies based on imitation, a behavior rule widely applied in human societies consisting of imitating successful behavior. We first develop two imitation-based spectrum access policies based on the basic Proportional Imitation (PI) rule and the more advanced Double Imitation (DI) rule given that a SU can imitate any other SUs. We then adapt the proposed policies to a more practical scenario where a SU can only imitate the other SUs operating on the same channel. A systematic theoretical analysis is presented for both scenarios on the induced imitation dynamics and the convergence properties of the proposed policies to an imitation-stable equilibrium, which is also the @math -optimum of the system. Simple, natural and incentive-compatible, the proposed imitation-based spectrum access policies can be implemented distributedly based on solely local interactions and thus is especially suited in decentralized adaptive learning environments as cognitive radio networks.
Imitating successful behavior is a natural and frequently applied approach when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic congestion games. We propose to study concurrent imitation dynamics that emerge when each player samples another player and possibly imitates this agents' strategy if the anticipated latency gain is sufficiently large. Our main focus is on convergence properties. Using a potential function argument, we show that these dynamics converge in a monotonic fashion to stable states. In such a state none of the players can improve their latency by imitating others. As our main result, we show rapid convergence to approximate equilibria. At an approximate equilibrium only a small fraction of agents sustains a latency significantly above or below average. In particular, imitation dynamics behave like fully polynomial time approximation schemes (FPTAS). Fixing all other parameters, the convergence time depends only in a logarithmic fashion on the number of agents. Since imitation processes are not innovative they cannot discover unused strategies. Furthermore, strategies may become extinct with non-zero probability. For the case of singleton games, we show that the probability of this event occurring is negligible. Additionally, we prove that the social cost of a stable state reached by our dynamics is not much worse than an optimal state in singleton congestion games with linear latency functions. While we concentrate on the case of symmetric network congestion games, most of our results do not explicitly use the network structure. They continue to hold accordingly for general symmetric and asymmetric congestion games when each player samples within his commodity.  We consider the problem of spectrum trading with multiple licensed users (i.e., primary users) selling spectrum opportunities to multiple unlicensed users (i.e., secondary users). The secondary users can adapt the spectrum buying behavior (i.e., evolve) by observing the variations in price and quality of spectrum offered by the different primary users or primary service providers. The primary users or primary service providers can adjust their behavior in selling the spectrum opportunities to secondary users to achieve the highest utility. In this paper, we model the evolution and the dynamic behavior of secondary users using the theory of evolutionary game. An algorithm for the implementation of the evolution process of a secondary user is also presented. To model the competition among the primary users, a noncooperative game is formulated where the Nash equilibrium is considered as the solution (in terms of size of offered spectrum to the secondary users and spectrum price). For a primary user, an iterative algorithm for strategy adaptation to achieve the solution is presented. The proposed game-theoretic framework for modeling the interactions among multiple primary users (or service providers) and multiple secondary users is used to investigate network dynamics under different system parameter settings and under system perturbation. Next-generation wireless networks will integrate multiple wireless access technologies to provide seamless mobility to mobile users with high-speed wireless connectivity. This will give rise to a heterogeneous wireless access environment where network selection becomes crucial for load balancing to avoid network congestion and performance degradation. We study the dynamics of network selection in a heterogeneous wireless network using the theory of evolutionary games. The competition among groups of users in different service areas to share the limited amount of bandwidth in the available wireless access networks is formulated as a dynamic evolutionary game, and the evolutionary equilibrium is considered to be the solution to this game. We present two algorithms, namely, population evolution and reinforcement-learning algorithms for network selection. Although the network-selection algorithm based on population evolution can reach the evolutionary equilibrium faster, it requires a centralized controller to gather, process, and broadcast information about the users in the corresponding service area. In contrast, with reinforcement learning, a user can gradually learn (by interacting with the service provider) and adapt the decision on network selection to reach evolutionary equilibrium without any interaction with other users. Performance of the dynamic evolutionary game-based network-selection algorithms is empirically investigated. The accuracy of the numerical results obtained from the game model is evaluated by using simulations. We consider non-cooperative mobiles, each faced with the problem of which subset of WLANs access points (APs) to connect and multihome to, and how to split its traffic among them. Considering the many users regime, we obtain a potential game model and study its equilibrium. We obtain pricing for which the total throughput is maximized at equilibrium and study the convergence to equilibrium under various evolutionary dynamics. We also study the case where the Internet service provider (ISP) could charge prices greater than that of the cost price mechanism and show that even in this case multihoming is desirable.