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In other words, the equilibrium points of G (if any) are equal to the equilibria of a modified (generalized) game, which differs from G as now the strategy space is the subset of P k such that any vector allocation p is such that p k ≥ p ̇ k, and hence, γ k ≥ γ ̇.
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We deduce that the vector of allocations x O [ v, m] is a solution to the equation D 2 [ v ] x I (m ) = - D 1 [ v ] x P [ v, m ] x O [ v, m ] for the input parameter vector x I (m ) = (0, …, 0, C (m ) v I (m ), 0, …, 0 ), where D1 and D2 are defined in Table 10.
., rate allocation vector, where is the rate allocated for session,., flow allocation vector for session, where is the session 's traffic routed through link., transmission schedule vector, where is the time fraction for the transmission mode.
Also, Φ is the frame allocation vector for a specific DoF vector of δ.
where A with element (a_{{k,n}}^{{m,v}}) and P with element (p_{{k,n}}^{{m,v}}) are the PRB allocation vector and the power allocation vector, respectively.
In our model, we define the following components for primary user y (PU y ): Spectrum allocation vector SP y : Spectrum allocation vector SP y : We model a channel as an ON/OFF where the ON period indicates the duration of PUs' activities.
As both the power allocation vector and the rate pair vector of an optimal schedule are unique, we conclude that the optimal schedule is unique under WUFBC.
For every channel state, there is a fixed continuous probability measure, where is the timeslot allocation vector and is the power allocation vector.
We deduce that D1 is invertible so that the vectors of allocations x O [ v, m] and x P [ v, m] are determined uniquely.
Variables (i), rate allocation vector, where is the rate allocated for session,.
For the allocation vector, however, it is not possible to summarize the sampled vectors in the same way as for the edges, because of the so called label switching problem.
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