Éva Tardos

Éva Tardos studies algorithms and the efficiency of systems in which participants act for themselves. Her work with Tim Roughgarden quantified inefficiency in selfish routing, relating equilibrium traffic to a centrally optimized flow.^[ref][ref]

A small example shows the issue. Route one unit of traffic over two parallel links, one with latency $x$ when carrying flow $x$ and one with fixed latency one. The selfish equilibrium sends everything over the first link, giving total latency one: no user can improve by switching to the other link. Splitting traffic equally gives total latency $\frac{1}{2}\cdot \frac{1}{2}+\frac{1}{2}\cdot 1=3/4$, which minimizes $x^2+1-x$. The equilibrium-to-optimum ratio is $4/3$.

This is a precise price of anarchy calculation. It demonstrates why individually sensible choices can create avoidable aggregate delay and why a guarantee about an optimization algorithm does not automatically describe an uncoordinated network.