Corollary 5.1 Let Γ = ( X i, f i ) i ∈ I be a noncooperative game with every f i being the payoff function of player i.
The formulated coalition game of the l-th sub-channel is denoted by (mathcal {G}^{l}=(mathcal {N}_{l},v)), where (mathcal {N}_{l}) is the set of players and (v: eta (mathcal {N}_{l})mapsto mathbb {R}) is the payoff function of the coalitions [21].
In this section, we will consider the multiobjective noncooperative game in its strategic form Γ = ( X i, V i ) i ∈ I, where I = { 1, 2, …, n } is the set of players; every X i is the strategy set of the i th player and every V i : X = ∏ i ∈ I X i → R k i is the payoff function of the i th player with k i being a positive integer.
Payoff functions ( left({boldsymbol{U}}_{{mathrm{APO}}_i}left(cdotp right),{boldsymbol{U}}_{mathrm{IoTM}}left(cdotp right)right) ): ( {boldsymbol{U}}_{{mathrm{APO}}_i} ) and U IoTM are the payoff functions of ( {mathbb{S}}_{mathrm{IoTM}} ) and ( {mathbb{S}}_{{mathrm{APO}}_i} ), respectively.
One difficulty is that the payoff function g has a discontinuous first derivative at the strike price K which will prevent the scheme from achieving the expected fourth-order convergence rate.
Therefore, four image quality assessment metric and correlation functions will be adopted in the payoff function for encoder player.
All the other predictions presented are independent of the payoff function.
These regions lie along a falling curve that represents a theoretical approximation, based on equation 3, that is independent of the payoff function.
A given game (mathcal {G} = langle {mathcal {N}, left {mathcal {A}_{n}right }, {f_{n}(x)}}rangle ) is equivalent to (VI(mathcal {A}, F)) if the following two conditions hold: (i) The strategy set (mathcal {A}_{n}) is closed and convex; (ii) the payoff function is convex and continuously differential for (x in mathcal {A}_{n}).
