as t goes to infinity and,

x˙1,t(s1)=x1,t(s1)[ER1(w,es1,β2,ϵ(x1,t))s1A1x1,t(s1)ER1(w,es1,β2,ϵ(x1,t))]

(4.20)

is the asymptotic pseudo-trajectory of {x1t}t0.

•  Assume that Player 1 is a slow learner of (M-IBG) and Player 2 is a fast learner of (IBG). Then almost surely,

x2tσ2,ϵ(x1)0,

as t goes to infinity and,

x˙1,t(s1)=x1,t(s1)[ER1(w,es1,σ2,ϵ(x1,t))

(4.21)

s1A1x1,t(s1)ER1(w,es1,σ2,ϵ(x1,t))],

(4.22)

is the asymptotic pseudo-trajectory of {x1t}t0.

4.4.3    Aggregative Robust Games in Wireless Networks

The focus of our analysis in this subsection is on aggregative games. In an aggregative game, the payoff of each player is a function of the player’s own action and of the sum of the actions (or, the weighted sum action) ...

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