## 4 Taxonomy: Classification of GT Approaches in Network Virtualization
### Game Goals
#### 4.2.2 Goal 2: Maximize the Power Allocation  
Moreover, the virtualization framework is proposed for wireless networks to support multiple heterogeneous self-interested services and improve their performance. Virtualization provides services decoupling from the wireless network infrastructure. The Wireless Virtual Network (WVN) consists of two entities: The infrastructure providers (InPs), owning all physical resources and the Virtual Network Operators (VNOs), which do not own any infrastructures or spectrum resources. The InPs share and manage their power resources with the VNOs, aiming to exploit multi-power resources from multi-owner to provide services to end-users by making their virtual networks (VN). As VNOs, the InP creates VN to serve its users called local slice and VNs generated by the VNOs\" users named foreign slice. The challenging key in the WVN environment is maximizing the resource allocation between the SPs by solving the optimization problem in terms of power allocation optimization.  
The authors in [21] start with the studying of the virtualization in the wireless network to end by solving the problem of physical resources competition between the SPs. Thus, the network operators (NO) manage and control the resource allocation by pricing each bid. The interaction between the NO and the SPs can be modeled as a sequential auction game where the SPs sequentially bid on the network resources (power resources). Thus, a theoretical price is introduced as a potential congestion level that an SP expects in the future. An efficient resource allocation under the proposed framework defined as a separation between SPs and the NO is achieved through the Nash equilibrium. Motivated by the game theory concept, the authors in [23] modeled the competition between the foreign slices as a non-cooperative game. Players in this game are foreign slices and the strategy of each player is the allocated power \(p_{i}\). Each foreign slice seeks to maximize its individual revenue. A price function is introduced to the game to establish the charge to be paid by the VNOs during the power allocation game. The utility function is presented in terms of cost by the following formula:  
\[\Phi_{i}(P)=\frac{L\times r\times f(y_{i})}{M\times p_{i}}-p_{i}\times c(P) \tag{4}\]  
where \(L\) bits are payloads in frames of \(M\) bits (\(M>L\)), \(f(y_{i})\) denotes the probability of correct reception of a frame at the receiver, \(r\) is the rate of transmission, \(p_{i}\) is the allocated power, and \(c\) is a function of the total amount of the available power. The optimization power allocation problem is solved through the Nash equilibrium. No foreign slice can increase its utility function by changing individual power selection with other foreign slices' given power. In other words, all the foreign slices can achieve the best response of the power selection.  
The work in [24] is interested in proposing two auction games as a solution for the power allocation optimization problem in the virtualization of the mobile cellular as well as decoupling the services and the infrastructure network. In the first non-cooperative auction game, the authors consider the interaction between two important entities: InPs and VOs, to build an interactional game model. In the proposed auction game, the bidders are defined as VOs competing for power resources, while the auctioneer is defined as the hypervisor (InPs). During the second cooperative game, the coalition's concept is established to maximize the payoff for all VOs. The users in a specific VO are modeled as players. Users who subscribed to the same VO can cooperate and form a coalition to maximize their gains against the other coalition. The two-stage game models tend to allocate the resource between the VOs fairly.