Florian Schoppmann

Exact Price of Anarchy for Polynomial Congestion Games

We show exact values for the worst-case price of anarchy in weighted and unweighted (atomic unsplittable) congestion games, provided that all cost functions are bounded-degree polynomials with nonnegative coefficients. The given values also hold for weighted and unweighted network congestion games.

Exact price of anarchy for polynomial congestion games

We show exact values for the price of anarchy of weighted and unweighted congestion games with polynomial latency functions. The given values also hold for weighted and unweighted network congestion games.

Voronoi Games on Cycle Graphs

In a Voronoi game, each of a finite number of players chooses a point in some metric space. The utility of a player is the total measure of all points that are closer to him than to any other player, where points equidistant to several players are split up evenly among the closest players. In a recent paper, Durr and Thang (2007) considered discrete Voronoi games on graphs, with a particular focus on pure Nash equilibria. They also looked at Voronoi games on cycle graphswith nnodes and kplayers. In this paper, we prove a new characterization of all Nash equilibria for these games. We then use this result to establish that Nash equilibria exist if and only if

Total latency in singleton congestion games

k \leq \frac{2n}3

Wardrop equilibria and price of stability for bottleneck games with splittable traffic

or ki¾? n. Finally, we give exact bounds of

Group-Strategyproof Cost Sharing for Metric Fault Tolerant Facility Location

\frac 94

To be or not to be (served)

and 1 for the prices of anarchy and stability, respectively.

New efficiency results for makespan cost sharing

We provide a collection of new upper and lower bounds on the price of anarchy for singleton congestion games. In our study, we distinguish between restricted and unrestricted strategy sets, between weighted and unweighted player weights, and between linear and polynomial latency functions.

The power of two prices: beyond cross-monotonicity

We look at the scenario of having to route a continuous rate of traffic from a source node to a sink node in a network, where the objective is to maximize throughput. This is of interest, e.g., for providers of streaming content in communication networks. The overall path latency, which was relevant in other non-cooperative network routing games such as the classic Wardrop model, is of lesser concern here. To that end, we define bottleneck games with splittable traffic where the throughput on a path is inversely proportional to the maximum latency of an edge on that very path-the bottleneck latency. Therefore, we define a Wardrop equilibrium as a traffic distribution where this bottleneck latency is at minimum on all used paths. As a measure for the overall system well-being-called social cost-we take the weighted sum of the bottleneck latencies of all paths. Our main findings are as follows: First, we prove social cost of Wardrop equilibria on series parallel graphs to be unique. Even more, for any graph whose subgraph induced by all simple start-destination paths is not series parallel, there exist games having equilibria with different social cost. For the price of stability, we give an independence result with regard to the network topology. Finally, our main result is giving a new exact price of stability for Wardrop/bottleneck games on parallel links with M/M/1 latency functions. This result is at the same time the exact price of stability for bottleneck games on general graphs.

The Power of Small Coalitions in Cost Sharing

In the context of general demandcost sharing, we present the first group-strategyproof mechanisms for the metric fault tolerant uncapacitated facility location problem. They are