A Survey of Client-Controlled HetNets for 5G <s> F. GAME THEORETIC ANALYSIS <s> 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. <s> BIB001 </s> A Survey of Client-Controlled HetNets for 5G <s> F. GAME THEORETIC ANALYSIS <s> This paper addresses the problem of network selection, which arises when wireless mobile users can choose among multiple available wireless access networks to connect to. In particular, we are interested in studying the dynamics of the competition among different selfish mobile users which operate the network selection with the goal of minimizing their own selection cost. To this extent, we formalize the problem as a non-cooperative game, and we study the quality of the corresponding Nash equilibria under three expressions for the users' selection cost by deriving tight analytical bounds on the price-of-anarchy and the price-of-stability for the games. Finally, we introduce a mathematical programming formulation for the games which allows one to compute the equilibria in realistic wireless access network topologies. <s> BIB002 </s> A Survey of Client-Controlled HetNets for 5G <s> F. GAME THEORETIC ANALYSIS <s> 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. <s> BIB003 </s> A Survey of Client-Controlled HetNets for 5G <s> F. GAME THEORETIC ANALYSIS <s> Nowadays networks are characterized by the abundance of diverse Radio Access Interfaces (RAI) in the same operating area. The various wireless interfaces can belong to the same Radio Access Technology or not. In such a scenario, a mobile user will be able to select selfishly one of the available radio interfaces in order to enhance its own performance. Therefore, the radio access selection policy is vital and must be designed astutely to avoid resource wastage. In this paper, the RAI selection process is apprehended as a congestion game which is a class of noncooperative games in which users share a common set of limited resources. The cost sustained by a given user depends upon the congestion impact inflected by other users sharing the same resource. Devising distributed resource sharing schemes that optimize user air interface selection depends crucially on the existence of Nash equilibria for the modelling congestion games. In this paper, we model the downlink access for three main broadband technologies (WiMAX, WiFi and 3.5G HSDPA) and study the existence of pure Nash equilibria for various multi-RAI scenarios involving those technologies. <s> BIB004
Noncooperative game theory, in which individual clients make local decisions to maximize individual payoffs without a means to enforce restrictions on the behavior of other clients, is often used for fully-distributed coordination without any sort of management from a non-client party-which is the case for Distributed RAT Selection. In this model, the set of players is the set of clients, and the set of player strategies is the set of BSs (or RATs) that they may associate with at a given time. A game of this type is said to have converged to a Nash Equilibrium (NE) if each player considers its selected strategy to be optimal given the choices of all other playersthat is, it cannot unilaterally improve its payoff by changing strategies. A common class of techniques for distributed coordination is found in the area of noncooperative congestion games BIB004 , BIB002 , where players select from a common set of strategies to play and the reward of each strategy is a monotonically nonincreasing function of the total number of players playing that strategy  . In BIB004 , by considering an entire type of RAT to be a single BS in a congestion game framework, a finite improvement path can be found for the congestion game where each asynchronous client can selfishly switch to reduce their cost until a NE is reached. However, to implement this, the authors caution that to reach a pure NE requires exact information on incurred cost, which may be difficult to obtain in a timely and accurate manner. The authors in BIB002 model downlink access to multiple broadband BSs as a congestion game, which models the client-and BS-specific cost of association as the congestion impact on other clients sharing the same network. By abstracting away the multi-rate property of HetNets, tight analytical bounds for the price of anarchy and price of stability (ratio between the value of the ''best/worst" equilibria points and an optimal solution) are found. Evolutionary games, in which groups of clients select strategies to play against clients from other groups, have also been considered BIB001 , BIB003 . In BIB001 , a population game for multihomed RAT association is studied for 802.11 under evolutionary dynamics. Prices based on channel occupancy and total throughput in the cell are used to calculate payoff functions for each client to calculate a potential function for the population game, and it is shown that the stationary points of such a game are asymptotically stable and maximizes throughput. In BIB003 , an evolutionary game is used to perform client-driven network load balancing between different types of networks (specifically WMAN, cellular, and WLAN). Two solutions to obtaining evolutionary equilibrium are presented. The population evolution solution relies on coordination between clients to share knowledge of the average payoff in a given area, so that underperforming clients may change networks; and reinforcement learning leverages Q-learning to explore and rank the different networks for optimal empirical payoff.