# Game-Based Resource Allocation Mechanism in B5G HetNets with Incomplete Information
## 4 Simulation Results
### Follower Game  
Given the initial printing strategies of the two networks, users in area 1 and area 2 played the resource competition game with the adjustment of their bandwidth requesting strategies to maximize their expected utilities.  
Figure 4 gives the adaptation trajectories of user strategies in area 1 and area 2. The \"Area 1\" curve shows the bandwidth strategies of users in area 1, which is covered only by WIMAX. The \"Area 2 (WIMAX)\" and \"Area 2 (WLAN)\" represent, respectively, the bandwidth requests from WIMAX and WLAN for users in area 2. As shown in this figure, the strategies of mobile users in either area 1 or area 2 tend to converge, which proves the existence of equilibrium in the follower game.  
Taking users in area 2 as an example, Figure 5 shows the impacts of different factors on the utility function, including the profit based on the throughput, the fee to request bandwidth, and the cost caused by the load of the connected network. The profit based on throughput and the fee to buy bandwidth both increased gradually with the increment of the user's bandwidth request, while the increasing load of networks caused the volatility in the user's cost curve till to an equilibrium value.  
The utility curves of mobile users in both area 1 and area 2 are shown in Figure 6. The utility of one mobile user in area 2 is higher than that in area 1. This phenomenon can be explained by the reason that mobile users in the area covered by multi-networks could acquire more resources than the users  
Figure 4: Bandwidth requesting strategy with the number of iterations.  
Figure 5: Payoff and costs of mobile user in area 2 with the number of iterations.  
served by only one network. Furthermore, the curve of mobile user's utility in area 2 fluctuated till it reached a stable value, which was caused by the adjustment of the user's strategy with the changes in the load of networks.  
Figure 7 analyzes the impact of the number of users on the utilities of users in area 1 and area 2, respectively. The X-axis is the number of users in area 2. We conducted this simulation considering the practical situation that the number of users in a hot spot region (i.e., area 2) will increase as time goes long. In this case, the utilities of users both in the two areas decreased with the increasing number of players in the follower game. But it is obvious to see that the descent rate of users in area 2 was faster than the users in area 1. The reason is that the increment of the number of users in area 2 had a more serious impact on the load of the WLAN and users may have adjusted their strategies to request more bandwidth from WIMAX.  
The average utilities of all users obtained from BNE in an incomplete information game and the Nash equilibrium (NE) in a complete information game are shown in Figure 8. Here, the NE with complete information referred to the actual average utility when users perfectly knew the channel gain of each other. Note that the average utility obtained from BNE with incomplete information was lower than that from the NE with complete information. The reason can be explained via the fact that the users' expected average utility obtained by probabilistic prediction was less accurate than the actual average utility obtaining in a complete information game.  
Figure 6: Utility of the mobile user in either area 1 or area 2 with the number of iterations.  
Figure 7: Utility of the mobile user in either area 1 or area 2 with the number of users in area 2.