## 7 Simulation Results
### Performance Evaluation in a MANET Scenario
#### 7.2.4 Behaviour of \(p_{i}^{*}\)  
It is important to analyze the behavior of \(p_{i}^{*}\) when the fraction of packet losses through the best or through the medium-quality paths (\(FPL_{b}\) or \(FPL_{m}\)) changes. We can easily guess that if the packet losses through the best path (_i.e._, \(FPL_{b}\)) increases, the probability to sent (I+P) frames through that best path \(p_{i}^{*}\) should decrease, so more (I+P) packets would be sent through the medium-quality path. On the other hand, if the packet losses through the medium path (_i.e._, \(FPL_{m}\)) increases, \(p_{i}^{*}\) should increase, so more (I+P) packets would be sent through the best path.  
A way to check this logical behavior is to analyze an interval of time of a simulation where jitter and losses behave almost constant in one path (best or medium-quality path) and see how jitter and losses in the other path behave. However, it was impossible to find such an interval. Due to that, we decided to prove it mathematically taking some values of our simulations as inputs. This will help us to analyze the \(p_{i}^{*}\) behavior when \(FPL_{b}\) or \(FPL_{m}\) changes, which are shown in Figures 16 and 17. As we can see, we only study the behavior of \(p_{i}^{*}\) as a function of the \(FPL\) till 40% of packet losses since above that threshold it is considered as a non interest range. We show the average results of three different simulations.  
Figure16 depicts the behavior of the best response probability \(p_{i}^{*}\) of sending I+P frames through the best path for player \(i\) when the fraction of packet losses (\(FPL\)) through the medium-quality path \(FPL_{m}\) increases. It is important to mention that as \(FPL_{m}\) increases, \(p_{i}^{*}\) increases as well. The reason is that when \(FPL_{m}\) increases that means that we are loosing more packets in the medium-quality path, so we should better send the packets through the best path (_i.e._, increase \(p_{i}^{*}\)) in order to alleviate the congestion in the medium-quality path.  
In the same way, Figure 17 depicts the behavior of the best response probability \(p_{i}^{*}\) of sending I+P frames through the best path for player \(i\) (_i.e._, \(p_{i}^{*}\)) when the fraction of packet losses (\(FPL\)) through the best quality path \(FPL_{b}\) increases. We can see that when \(FPL_{b}\) increases, \(p_{i}^{*}\) decreases. The reason is that when \(FPL_{b}\) increases that means that we are loosing more packets in the best path, so we should send more packets through the medium-quality pat (_i.e._, decrease \(p_{i}^{*}\)) in order to avoid congestion in the best path.  
For further information about how we obtained Figures 16 and 17, please see the Appendix B.  
In the next section, we present an initial performance evaluation of our proposal in a VANET scenario to show the benefits of our approach in this kind of vehicular scenario. As pointed out in Section 8, we are currently developing a multi-user game-theoretical geographic routing protocol specifically designed to cope with the inherent issues of VANETs, and that will be based on this current work as a starting point.  
Figure 15: Utility function graph for player 1 and 2. (**a**) Player 1; (**b**) Player 2.