  In bandwidth allocation, competing agents wish to transmit data along paths
of links in a network, and each agent's utility is equal to the minimum
bandwidth she receives among all links in her desired path. Recent market
mechanisms for this problem have either focused on only Nash welfare, or
ignored strategic behavior. We propose a nonlinear variant of the classic
trading post mechanism, and show that for almost the entire family of CES
welfare functions (which includes maxmin welfare, Nash welfare, and utilitarian
welfare), every Nash equilibrium of our mechanism is optimal. We also prove
that fully strategyproof mechanisms for this problem are impossible in general,
with the exception of maxmin welfare. More broadly, our work shows that even
small modifications (such as allowing nonlinear constraints) can dramatically
increase the power of market mechanisms like trading post.
