Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified network for rate $r$ and \Copt(r) denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192

Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified network for rate $r$ and \Copt(r) denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201

Personalized Tourist Route Generation

When tourists are at a destination, they typically search for information in the Local Tourist Organizations. There, the staff determines the profile of the tourists and their restrictions. Combining this information with their up-to-date knowledge about the local attractions and public transportation, they suggest a personalized route for the tourist agenda. Finally, they fine tune up this route to better fit tourists' needs. We present an intelligent routing system to fulfil the same task. We divide this process in three steps: recommendation, route generation and route customization. We focus on the last two steps and analyze them. We model the tourist planning problem, integrating public transportation, as the Time Dependent Team Orienteering Problem with Time Windows (TDTOPTW) and we present an heuristic able to solve it on real-time. Finally, we show the prototype which generates and customizes routes in real-time

Algorithmic Game Theory and Networks

In this thesis we are studying three different problems that belong to the intersection of Game Theory and Computer Science. The first concerns the design of efficient protocols for a Contention Resolution problem regarding selfish users who all need to transmit information over a common single–access channel. We will provide efficient solutions for different variants of the problem, depending on the feedback that the users can receive from the channel. The second problem concerns the Price of Stability of a fair cost sharing Network Design problem for undirected graphs. We consider the general case for which the best known upper bound is the Harmonic number Hn, where n is the number of players, and the best known lower bound is 12=7 ~ 1:778. We improve the value of the previously best lower bound to 42=23 ~ 1:8261. Furthermore, we study two and three players instances. Our upper bounds indicate a separation between the Price of Stability on undirected graphs and that on directed graphs, where Hn is tight. Previously, such a gap was only known for the cases where all players shared a terminal, and for weighted players. Finally, the last problem applies Game Theory as an evaluation tool for a computer system: we will employ the concept of Stochastic Stability from Evolutionary Game Theory as a measure for the efficiency of different queue policies that can be employed at an Internet router

New Existence Proofs for Epsilon-nets

We describe a new technique for proving the existence of small \eps-nets for hypergraphs satisfying certain simple conditions. The technique is particularlyuseful for proving o(\frac{1}{\eps}\log{\frac{1}{\eps}}) upper bounds which is not possible using the standard VC dimension theory. We apply the technique to several geometric hypergraphs and obtain simple proofs for the existence of O(\frac{1}{\eps}) size \eps-nets for them. This includes the geometric hypergraph in which the vertex set is a set of points in the plane and the hyperedges are defined by a set of pseudo-disks. This result was not known previously. We also get a very short proof for the existence of O(\frac{1}{\eps}) size \eps-nets for half\-spaces in $\Re^3$