## 4 Taxonomy: Classification of GT Approaches in Network Virtualization
### Game Goals
#### 4.2.3 Goal 3: Fairly Allocate the Physical Resource  
The fairness of the resources assignment is a very indispensable challenge faced the resource virtualization. Many solutions are proposed to satisfy all the resources claimants by achieving the allocation fairness. Authors in [26] introduced a dynamic game scheme with imperfect information to model the competitive and braining behavior among multiple cloud users. The proposed game model addresses the resource allocations problem in the competitive cloud environment. Thus, they designed a new resource pricing model based on the learning concept to predict the price of future resource allocation and satisfy the constraints related to the resource and the budget. The Nash equilibrium is investigated as a solution for the auction game to achieve the best response for all network users. This work proved that, besides the budget constraints, any bid also depends on its workload. As well as the previous proposal, the work in [27] studied the same problem of resource allocation and pricing policies in cloud computing. Firstly, the authors formulated this problem as a non-cooperative bargaining game model. The players are the computation-intensive tasks competing for the allocation of many Virtual CPU Instances (VCI). Thus, the tasks need to satisfy certain constraints such as deadline and/or budget. To meet those requirements and to solve the previous problem, Nash Bargaining Solution (NBS) and Raiffa Kalai-Smorodinsky Bargaining Solution (RBS) are investigated where the goal is to minimize the executed time of tasks and to maximize the revenue based on the principle of pricing the mechanism. The same tenet is adopted by the work in [22] where a cooperative game model is proposed to fairly allocate the resource between VMs. The allocation fairness concept is achieved through two fundamental objectives: to guarantee bandwidth for all the VMs according to the bandwidth requirements and to share the residual bandwidth in proportion to the weights of VMs. A bargaining game is introduced for the data-center networks to fairly allocate the bandwidths to players (VNs) by meeting the announced objectives. The VNs cooperate with each other to achieve a win-win solution, so-called, Pareto optimality where all pair-VNs involved in the game obtain the best profit. In this game, the VM-pairs are considered as players competing for limited bandwidth resources in data-centers. The authors introduce the Nash bargaining solution to solve the optimization problem. The virtualization technologies in the cloud center lead to virtualizing the different physical resources (CPU, storage, memory, substrate links, bandwidths, and power). The sharing concept in cloud computing makes resource allocation a fundamental problem, which is treated in work [28]. A new resource allocation scheme is introduced for the cloud computing network based on the combination of the Stackelberg game and the hidden Markov model. The proposed approach aims at ensuring the resource allocation fairness between the SPs. In this competitive cloud environment, the SPs compete to rent enough resources from infrastructure suppliers (INs) to create virtual networks, and provide the services to end-users. Seeking for stable equilibrium, each SP tries to solve the optimization problem of the dynamic Stackelberg pricing game by minimizing the predicted cost of the requested resource of the CPU, bandwidth, and storage. Moreover, the authors in [32] studied the cloud-based service as the interaction between the Software as a Service (SaaS) providers hosting their applications in the Infrastructure as a Service (IaaS) provider. They modeled the two conflicting situation based on the game theory perspective. In the first situation, each SaaS competes with the others to allocate enough resources from IaaS. In the second situation, the IaaS intends to maximize its profit defined as the revenues obtained from providing the resources to the SaaS.