on the approximation (easier and faster to implement) will give more resources than the minimum required, but the achieved capacity is always taken from the full equation. The problem then is to determine how best to allocate the minimum number of RBs to each user SO they achieve the necessary sSINR to meet their QoS requirements, subject to Figure 8.9 Approximation to Shannon. SNR (dB) Shannon Approximation 8.4 Radio Resource Allocation that Considers Spectrum Sharing (i) the interference seen by that user, (ii) the channel conditions to that user, and (iii) users in other cells being allocated resources at the same time. In Liu et al. [39] the entity allocating the resource was the cell but here the situation is more complex, depending on which model of sharing is used: it may be the slice rather than the cell as explained later. The term resource allocation entity (RAE) is used as a more general description that may refer to the cell or the slice. The game allows each RAE to maximize its number of qualified users by choosing the best allocation of RBs, while competing against the allocation schemes of other RAE. The max- imum is reached when all RAEs maintain their current positions. Non-cooperative game theory is suitable for modeling this type of multi-person problem characterized by strate- gic interdependency [43] although the solution may be suboptimal [44]. This allows an RAE to be fully in charge of resource allocation independently of other RAEs (although dependent on the interference generated by the other RAEs) and SO avoids the overhead of message exchange between RAEs. Compared with other optimization techniques, it can achieve much faster convergence and can be easily applied in practice although it might cause suboptimal solutions. The Nash Equilibrium [44] is regarded as the solution to a non-cooperative game; it consists of every player's best response against all others' strate- gies. In other words, it is a steady-state point where none of the players has an incentive to change their strategy