## 4 A Game-Theoretical Routing Protocol for MANETs
### The Bases of Our Proposal  
Figure 4 shows the proposed architecture. We assume \(N\) connections (\(S_{1}\)-\(D_{1}\), \(S_{2}\)-\(D_{2}\),..., \(S_{N}\)-\(D_{N}\)) and three paths. It is likewise possible to apply the proposal to any MANET independently of the number of connections, nodes and paths.  
Traditionally, nodes always would try to send the most important video frames through the best available path obtained by the multipath routing protocol. This means that I frames, which are the biggest ones and carry the most important video information, will be sent through the best path, whereas the least important frames (_i.e._, B frames) will be sent through the worst one. Nevertheless, if each node sends the most important frames through the best path, this path could get congested. As a consequence, that best path could suffer more losses than the others, which would lead to classify it as a worse path.  
Figure 4: Proposed framework to send the video frames.  
This behavior could produce an oscillatory performance that might affect the video experience of users if it happened frequently.  
To cope with this issue, users could _play a game_ such that the best two paths (best, medium) could be selected by each player to transmit the most important video frames (_i.e._, I+P frames). That is, each user could prefer to send sometimes the most important frames through the medium-quality path. Just for simplicity, B frames are considered always to be sent through the third path, which is the worst one. Also, I and P frames belonging to the same video stream are going to be sent through the same path to make more evident the inconveniences of sharing the same path, since there are more P frames than I frames per flow.  
Figure 5: Three possible allocation situations after playing the game. \(F\) and \(M\) represent the number of (I+P) and B frames to be sent, respectively. All the B frames are always sent through the worst path. (**a**) All the I+P frames are sent through the best path; (**b**) All the I+P frames are sent through the medium-quality path; (**c**) I+P frames will be sent through the best path with a certain probability \(p\) and through the second best path with a probability _I-p_. \(F_{1}\) and \(F_{2}\) represent the number of (I+P) frames sent through the best path and the medium-quality path, respectively, being \(\textit{F}=F_{1}+F_{2}\).  
In our game, in each iteration, users select paths for their respective video flows. As it is shown in Figure 5, we have three possible situations. Without playing the game, all users would always send the important frames through the best path (Figure 5a). Alternatively, they could play our routing game. Notice that case (Figure 5b) is worse than (Figure 5a) for all users since they are sending their frames together through the medium-quality path (this should not happen often). In the third case (Figure 5c), I+P frames will be sent through the best available path by each user with a certain probability \(p\) and through the second best path available with a probability \(1-p\).  
Notice that players (users) must decide their choices simultaneously and without communicating with each other. If we have a number of I+P frames equal to \(F\) to be sent, depending on the \(p\) value, a number of I+P frames equal to \(F_{1}\) will be sent through the best path and a number of I+P frames equal to \(F_{2}\) will be sent through the medium-quality one, being \(F=F_{1}+F_{2}\). \(M\) represents the number of B frames to be sent, always through the worst path.  
In the next section we will compute the optimal probability \(p\) (called \(p^{*}\)) of sending I+P frames through the best path that produces the best outcome for each player.