Dynamic Sharing of Wireless Spectrum by Haibo Zhou Quan Yu Xuemin (Sherman) Shen Shaohua Wu & Qinyu Zhang

Author:Haibo Zhou, Quan Yu, Xuemin (Sherman) Shen, Shaohua Wu & Qinyu Zhang
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.10)

Theorem 2

For , to form coalition in the set of , the equilibrium under the constraint of SAR can be reached when maximizing , where .

Proof

The coalition forming process of TFB providers is similar to that of TFB demanders. For the cooperation among TFB demanders in Case 1, the objective function is linear with the required size of TFB from the demanders and constrained by the packing upperbound, i.e., the capacity of provided TFBs. For any rational player , , when maximizing , where , all the players will have no incentive to join a new coalition. Obviously, the optimal formed coalition can approach to the equilibrium state, i.e., , to aggregate to be a renewed TFB with the demanded size of time-frequency block. Hence, once the minimal waste of redundant time-frequency space in TFB is approached, the maximal payoff of will be achieved, and the coalition forming equilibrium will be reached.

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