and denote the strategy space of user and all the users other than, respectively.
Let Y denote the strategy or commodity space, where Y is a separable Banach space.
Let C i ⊂ R + : = { x ∈ R ∣ x ≥ 0 } ( i = 1, …, n ) denote the strategy set of the firm i.
For each i ∈ I, let K i, f i 0, f i denote the strategy set and initial payoff value and payoff function of player i, respectively.
Now, let denote the strategy profile where all players play except player who plays, we can then describe player 's payoff as (8).
For each (Lsubseteq K), let (s_L = left( s_kright) _{kin L}) denote a strategy profile for bookmakers in L. Analogously, for each ({mathcal {C}} subseteq {mathcal {B}}), let (s_{{mathcal {C}}}(cdot ) = left( s_i(cdot )right) _{iin {mathcal {C}}}) denote a strategy profile for bettors in ({mathcal {C}}).
Let (tilde {sigma }^{R}_{n}) denote a strategy where consumer n deviates to some ({a^{d}_{n}} > a^{text {PO}}_{n}) in the current review phase and follow the review strategy afterwards and all consumers follow σ R all the time.
Denote the strategy of each D2D user or relay (n in mathcal {N}) by (x_{n} in mathcal {X}_{n}), where (mathcal {X}_{n} = {1,2,dots,C}) is a set of all feasible strategies of D2D user or the relay.
We also define x=(x 1,x 2,…,x N )=(x n,x −n ) to denote the strategy vector and (mathcal {X}) is the set of all possible x.
For each i ∈ I, let K i, f i 0 denote the strategy set and initial payoff value of player i, respectively, and let the real function f i : K ↦ R denote the payoff function of player i. Denote K = ∏ i = 1 n K i, K i ˆ = ∏ j ≠ i, j = 1 n K j.
