Table 1 Summary of symbols and notations

R(k,w)

Total secure data rate provided by Relay k at state w

s _i

Signal to User i

r _i

Relay selected by User i

N _k

Number of users choosing Relay k at the end of the game

M _i

Grouping results of relays before User i

M _i,k

Number of users before User i choosing Relay k

n _i,k

Number of users choosing Relay k since User i

h _i

Signal history obtained by User i

Pr(s _i |w)

Probability for User i to get the signal s _i , given relay true state w

vg(i)

Prior relay state distribution estimated by User i

U _i (R(k,w), N _k )

Utility of User i by choosing Relay k

Pr(n _i,k = y| M _i ,, h _i ,s _i )

Distribution of the number of users selecting Relay k after User i

P _a

Average accuracy of the signals

P _miss

Probability for a specified user to deviate from the CRG strategy