# Game-Based Resource Allocation Mechanism in B5G HetNets with Incomplete Information
## 2 System Model  
The Stackelberg game is a hierarchical decision-making game, in which the players who enforce their strategies on the other players are called 'leaders', while the players who respond to the leader's actions are called 'followers'. In a leader-follower Game, the followers are rational, and they will act to optimize their own payoff given the leader's strategies. However, considering the difficulty to obtain the core information of others in a particular situation, a Bayesian approach offers the possibility to solve the game with incomplete information. In the Bayesian game, a probability distribution is used to express the belief about the private information of others, which is indicated as the type of player. A game-based resource allocation model in a two-stage heterogeneous wireless network consisting of multiple networks and multiple mobile users is illustrated in Figure 1.  
Without loss of generality, we consider service area 1 to be covered only by network 1 (Net 1), while area 2 is covered both by Net 1 and network 2 (Net 2). In this model, network operators acting as the leaders provide users with limited bandwidth and play by properly setting price strategies to maximize their own profits, while mobile users play in the second stage, acting as the followers  
Figure 1: System model of the proposed mechanism. to adjust the need of bandwidth, according to the strategies of different operators and their payoff functions. In this model, we consider the practical situation where the channel gain between a mobile user and its associated network receiver is available for this user only, regarded as the type of user. Without loss of generality, we assumed that the communication between user and network can be uplinked or downlinked. The SINR (signal-to-interference-and-noise-ratio) received by a user is given as follows:  
\[\gamma_{i}=\frac{p_{i}\cdot h_{ij}}{\sum_{kqi}p_{k}\cdot h_{kj}+{\sigma_{0}}^{ 2}} \tag{1}\]  
where \(i\) randomly represents a user in the user set \(N=\{1,2,\ldots,n\}\), \(j\) represents a network operator in set \(M=\{1,2,\ldots,m\}\), \(p_{i}\) is the transmission power of user \(i\), \(h_{ij}\) is the channel gain from the user \(i\) to the network \(j\), and \({\sigma_{0}}^{2}\) is the noise power. We assume that the noise power is the same to all users. The throughput of user \(i\) obtained from network \(j\) is  
\[C_{ij}=q_{ij}\cdot\log_{2}(1+\frac{p_{i}\cdot h_{ij}}{\sum_{kqi}p_{k}\cdot h_{ kj}+{\sigma_{0}}^{2}}) \tag{2}\]  
where \(q_{ij}\) is the bandwidth of user \(i\) acquired from network \(j\). In order to prevent network congestion, the sum of the bandwidth requests in the coverage area of network \(j\) must not exceed a maximum level. This constraint can be expressed as in Equation (3), where \(W_{j}\) is the capacity of network \(j\). \[0\leq q_{ij}\leq W_{j},\sum_{i=1}^{n}q_{ij}\leq W_{j} \tag{3}\]  
In this model, \(m\) network operators are competing for \(n\) users in their covered areas. Regardless of other cost, the utility of network \(j\) is given in Equation (4), which considers only its pure profit based on the price of bandwidth. \[u_{j}^{L}=Q_{j}\cdot b_{j} \tag{4}\]  
where \(b_{j}\) is the price strategy of network \(j\) and \(Q_{j}\) is the load of network \(j\), defined as the total bandwidth of users who are connected to network \(j\), which is \(Q_{j}=\sum\limits_{i=1}^{n}q_{ij}\). It is obvious that the network wishes to maximize its profit by choosing an optimal bandwidth price strategy. If the price is too high, mobile users may change over to other networks, while, if too low, the profit may be also decrease, even though the network has come to saturation. The competition among users plays as a noncooperation game with incomplete information. The utility of the mobile user is composed of the profit based on the throughout and expense.