Bottleneck Routing Games with Low Price of Anarchy

We study {\em bottleneck routing games} where the social cost is determined by the worst congestion on any edge in the network. In the literature, bottleneck games assume player utility costs determined by the worst congested edge in their paths. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the size of the network. In order to obtain smaller price of anarchy we introduce {\em exponential bottleneck games} where the utility costs of the players are exponential functions of their congestions. We find that exponential bottleneck games are very efficient and give a poly-log bound on the price of anarchy: $O(\log L \cdot \log |E|)$, where $L$ is the largest path length in the players' strategy sets and $E$ is the set of edges in the graph. By adjusting the exponential utility costs with a logarithm we obtain games whose player costs are almost identical to those in regular bottleneck games, and at the same time have the good price of anarchy of exponential games.Comment: 12 page

LNCS

In resource allocation games, selfish players share resources that are needed in order to fulfill their objectives. The cost of using a resource depends on the load on it. In the traditional setting, the players make their choices concurrently and in one-shot. That is, a strategy for a player is a subset of the resources. We introduce and study dynamic resource allocation games. In this setting, the game proceeds in phases. In each phase each player chooses one resource. A scheduler dictates the order in which the players proceed in a phase, possibly scheduling several players to proceed concurrently. The game ends when each player has collected a set of resources that fulfills his objective. The cost for each player then depends on this set as well as on the load on the resources in it – we consider both congestion and cost-sharing games. We argue that the dynamic setting is the suitable setting for many applications in practice. We study the stability of dynamic resource allocation games, where the appropriate notion of stability is that of subgame perfect equilibrium, study the inefficiency incurred due to selfish behavior, and also study problems that are particular to the dynamic setting, like constraints on the order in which resources can be chosen or the problem of finding a scheduler that achieves stability

Congestion Games with Complementarities

We study a model of selfish resource allocation that seeks to incorporate dependencies among resources as they exist in modern networked environments. Our model is inspired by utility functions with constant elasticity of substitution (CES) which is a well-studied model in economics. We consider congestion games with different aggregation functions. In particular, we study $L_p$ norms and analyze the existence and complexity of (approximate) pure Nash equilibria. Additionally, we give an almost tight characterization based on monotonicity properties to describe the set of aggregation functions that guarantee the existence of pure Nash equilibria.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-57586-5_1

Flufenamic acid blocks depolarizing afterpotentials and phasic firing in rat supraoptic neurones

Depolarizing afterpotentials (DAPs) that follow action potentials in magnocellular neurosecretory cells (MNCs) are thought to underlie the generation of phasic firing, a pattern that optimizes vasopressin release from the neurohypophysis. Previous work has suggested that the DAP may result from the Ca2+-dependent reduction of a resting K+ conductance. Here we examined the effects of flufenamic acid (FFA), a blocker of Ca2+-dependent non-selective cation (CAN) channels, on DAPs and phasic firing using intracellular recordings from supraoptic MNCs in superfused explants of rat hypothalamus. Application of FFA, but not solvent (0.1 % DMSO), reversibly inhibited (IC50 + 13.8 μm; R + 0.97) DAPs and phasic firing with a similar time course, but had no significant effects (P > 0.05) on membrane potential, spike threshold and input resistance, nor on the frequency and amplitude of spontaneous synaptic potentials. Moreover, FFA did not affect (P > 0.05) the amplitude, duration, undershoot, or frequency-dependent broadening of action potentials elicited during the spike trains used to evoke DAPs. These findings suggest that FFA inhibits the DAP by directly blocking the channels responsible for its production, rather than by interfering with Ca2+ influx. They also support a role for DAPs in the generation of phasic firing in MNCs. Finally, the absence of a depolarization and increased membrane resistance upon application of FFA suggests that the DAP in MNCs may not be due to the inhibition of resting K+ current, but to the activation of CAN channels

A Unifying Tool for Bounding the Quality of Non-cooperative Solutions in Weighted Congestion Games

We present a general technique, based on a primal-dual formulation, for analyzing the quality of self-emerging solutions in weighted congestion games. With respect to traditional combinatorial approaches, the primal-dual schema has at least three advantages: first, it provides an analytic tool which can always be used to prove tight upper bounds for all the cases in which we are able to characterize exactly the polyhedron of the solutions under analysis; secondly, in each such a case the complementary slackness conditions give us an hint on how to construct matching lower bounding instances; thirdly, proofs become simpler and easy to check. For the sake of exposition, we first apply our technique to the problems of bounding the prices of anarchy and stability of exact and approximate pure Nash equilibria, as well as the approximation ratio of the solutions achieved after a one-round walk starting from the empty strategy profile, in the case of affine latency functions and we show how all the known upper bounds for these measures (and some of their generalizations) can be easily reobtained under a unified approach. Then, we use the technique to attack the more challenging setting of polynomial latency functions. In particular, we obtain the first known upper bounds on the price of stability of pure Nash equilibria and on the approximation ratio of the solutions achieved after a one-round walk starting from the empty strategy profile for unweighted players in the cases of quadratic and cubic latency functions. We believe that our technique, thanks to its versatility, may prove to be a powerful tool also in several other applications