From: Resource allocation in a MAC with and without security via game theoretic learning
Symbol | Definition |
---|---|
K | Number of transmitting users |
\(\widetilde {H}_{i}(t)\) | Channel gain to Bob |
\(\widetilde {G}_{i}(t)\) | Channel gain to Eve |
M | Possible values of channel gain |
\(\mathcal {P}_{i}\) | Action space |
\(\overline {P}_{i}\) | Power constraint for user i |
π(i) | ith element of permutation |
of index set | |
\(\alpha _{i}^{(j)}\) | pmf of H i (t) |
n | Maximum no. of action of a user |
\(\omega _{i}^{(t)}\left (a_{i}^{(t)},H_{i}(t)\right)\) | Instantaneous reward for user i |
for given action \(a_{i}^{(t)}\) | |
r i | Rate of user i |
\(\beta _{i}^{(j)}\) | pmf of Eve’s channel state, G i (t) |
Φ i (t) | Empirical distribution |
over action space for user i | |
a i | action choosen by user i |
δ i | Disagreement value for user i |
η b (t) | AWGN at Bob |
η e (t) | AWGN at Eve |
\(\mathcal {J}(\mathbf {r})\) | Jain’s index |
\(\mathfrak {C}(a_{i},a_{-i})\) | Cost of each user |
c(a i )(t) | Average cost of user i up to time t |
ε | Regret for cost minimization game |
ε ′ | Weight update factor |
\(\mathbbm {1}_{\{A\}}\) | Indicator function |
\(\mathcal {V}\) | Utility set for Nash bargaining |
Δ | Disagreement strategy for |
Nash bargaining solution | |
δ i | Disagreement value for user i |