Consider a network with two strategic users

sharing a same link with capacity c $=1.$ The utility function of user i is i $$

i

$($xi

$+1),$ where xi is the

rate allocated to user i$.$ Each user bids an amount that it is willing to pay, say wi for user i$,$ and

user i is allocated a data rate given by xi $=$ wi$/($w$1+$w$2).$ Thus, the payoff to user i is i $$

i

x

i

$$wi $.$

We assume $1=1$ and $2=2.$