Heike Sperber

We study the efficient computation of Nash and strong equi-libria in weighted bottleneck games. In such a game different players interact on a set of resources in the way that every player chooses a sub-set of the resources as her strategy. The cost of a single resource depends on the total weight of players choosing it and the personal cost every player tries to minimize is the cost of the most expensive resource in her strategy, the bottleneck value. To derive efficient algorithms for finding Nash equilibria in these games, we generalize a tranformation of a bottleneck game into a special con-gestion game introduced by Caragiannis et al. [1]. While investigating the transformation we introduce so-called lexicographic games, in which the aim of a player is not only to minimize her bottleneck value but to lexicographically minimize the ordered vector of costs of all resources in her strategy. For the special case of network bottleneck games, i.e., the set of resources are the edges ...

We consider the problem of routing traffic by selfish users in a net-work G = (V, E) with load-dependent nondecreasing latency functions ℓe on the edges. Each network user routes its traffic on a path of minimum latency, given the latency on the edges caused by the other users. It is known that under standard assumptions the routes chosen by the users forms a Nash equi-librium which, in general, is different from the global optimum. Both, a Nash equilibrium and the optimum, can be computed in polynomial time by convex programming, provided the latency functions are also differentiable. We give simple polynomial algorithms which for a series-parallel graph G with affine latency functions ℓe(x) = aex + be explicitly construct as functions of the total traffic r to be routed (i) the common latency LG(r) experienced by the users in a Nash equilibrium, (ii) for each edge e ∈ E the flow fe(r) on e in a Nash equilibrium , and (iii) a Nash flow and a global optimum (minimum latency) flow.

... Selfish bin coloring Leah Epstein · Sven O. Krumke · Asaf Levin · Heike Sperber © Springer Science+Business Media, LLC 2010 ... Epstein and Kleiman (2009) analyzed the price of anarchy and stability as well as the strong price of anarchy and stability. ...