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Table 1 Nomenclature

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