Table 1 Parameters used in the proposed algorithm

CS

Cloud server

F-APs

Fog-computing-based access points

MUs

Mobile users

ENs

Edge nodes

ℕ

The finite set of superordinated game players

ℛ _CS

The total spectrum resources of CS

δ _i

The allocated spectrum amount for the F ‐ AP _i

δ _i (t − Δt)

The δ _i value at the time period [t − Δt].

U _i (Δt)

The payoff received by the F ‐ AP _i during the recent Δt time period

\( {\mathbb{M}}_{\mathrm{i}} \)

The finite set of subordinated game players

ℜ _i

The set of F ‐ AP _i ‘s resources

C _i

The computation capacity in the F ‐ AP _i

σ _i

The placed cache files in the F ‐ AP _i

\( {\mathrm{U}}_{\mathrm{j}}^{\mathrm{i}} \)

The \( {\mathrm{MU}}_{\mathrm{j}}^{\mathrm{i}} \) ‘s payoff received by the F ‐ AP _i

β

The parameter weighs the past experience by considering a trust decay over time

ϕ

The parameter specifies the impact of past experience

T _i (t)

At time t, the F ‐ AP _i ‘s trust assessment

\( {\mathrm{F}}_{\mathrm{KSBS}}^{\mathrm{t}} \)

KSBS at time t

d = (d ₁, .. d _n)

Disagreement point when players cannot reach an agreement

\( {\upomega}_{\mathrm{i}}^{\mathrm{t}} \)

The player F ‐ AP _i ‘s bargaining power at time t

ℝⁿ

A jointly feasible utility solution set

τ

Factor to characterize the file popularity

\( \mathbb{M}= \) {ℳ₁.. ℳ _L }

A multimedia file set consists of L popular multimedia files

\( \mathcal{Q}=\left[{\mathrm{\mathcal{M}}}_1,\dots, {\mathrm{\mathcal{M}}}_{\mathrm{L}}\right] \)

Vector to represent the popularity distribution among \( \mathbb{M} \)

\( \mathbb{I}={\left[0,1\right]}^{\mathrm{n}\times \mathrm{L}} \)

A two-dimensional matrix to indicate the caching placement

\( {\mathcal{Z}}_{\mathrm{i}}^{\mathrm{l}} \)

The revenue from the lth file caching in the F ‐ AP _i ,

\( {\mathrm{\mathfrak{C}}}_{\mathrm{i}}^{\mathrm{l}} \)

The cost from the lth file caching in the F ‐ AP _i ,

\( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)

New service request of \( {\mathrm{MU}}_{\mathrm{j}}^{\mathrm{i}} \)

Min_S(\( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \))

The minimum spectrum requirement of \( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)

Min_C(\( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \))

The minimum computation requirement of \( {\Theta}_{\mathrm{j}}^{\mathrm{i}} \)

χ ⁱ

The currently using spectrum amount in the F ‐ AP _i

y ⁱ

The currently using computation amount in the F ‐ AP _i

\( {\mathfrak{X}}^{\mathrm{i}} \)

The current fronthaul transmission rate

\( {\mathfrak{M}}^{\mathrm{i}} \)

The maximum fronthaul transmission rate