On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

IR MPD CDF<SUB>3</SUB> in two-frequency IR fields

The effectiveness of various sets of laser frequencies was analyzed for two-frequency MPD of CDF3 molecule at the different pressures of buffer gas. It was shown that MPD yield increased compared to either single-frequency or two adjacent frequencies irradiation

Nash Social Welfare in Selfish and Online Load Balancing

In load balancing problems there is a set of clients, each wishing to select a resource from a set of permissible ones, in order to execute a certain task. Each resource has a latency function, which depends on its workload, and a client's cost is the completion time of her chosen resource. Two fundamental variants of load balancing problems are {\em selfish load balancing} (aka. {\em load balancing games}), where clients are non-cooperative selfish players aimed at minimizing their own cost solely, and {\em online load balancing}, where clients appear online and have to be irrevocably assigned to a resource without any knowledge about future requests. We revisit both selfish and online load balancing under the objective of minimizing the {\em Nash Social Welfare}, i.e., the geometric mean of the clients' costs. To the best of our knowledge, despite being a celebrated welfare estimator in many social contexts, the Nash Social Welfare has not been considered so far as a benchmarking quality measure in load balancing problems. We provide tight bounds on the price of anarchy of pure Nash equilibria and on the competitive ratio of the greedy algorithm under very general latency functions, including polynomial ones. For this particular class, we also prove that the greedy strategy is optimal as it matches the performance of any possible online algorithm

Probability, clinical decision making and hypothesis testing

Few clinicians grasp the true concept of probability expressed in the ‘P value.’ For most, a statistically significant P value is the end of the search for truth. In fact, the opposite is the case. The present paper attempts to put the P value in proper perspective by explaining different types of probabilities, their role in clinical decision making, medical research and hypothesis testing

A simple technique for the alignment of a ring resonator

A simple technique for the alignment of a ring resonator is presented. The positional and the directional alignments are obtained by the movements of independent mirrors. The effects of alignment inaccuracies on the performance of a ring resonator are discussed

Performance characteristics of a Nd: glass laser amplifier from fluorescence emission studies

The dependence of cavity transfer efficiency of a Nd: glass laser amplifier on flashlamp current density is obtained from the analysis of amplified fluorescence. The cavity transfer efficiency decreases as the current density through the flashlamps is increased. The use of the fluorescence method in optimizing the flashlamp pulse duration for achieving maximum gain in the amplifier is illustrated

Study of thermally induced active birefringence in Nd:glass laser rods

A study of active birefringence arising due to the thermal stresses in Nd:glass laser rods under different experimental conditions of pumping is reported. The extent of birefringence was measured in terms of depolarization of a pulsed probe beam from a Q-switched Nd:YAG (yttrium aluminum garnet) laser. The maximum depolarization for a 38-mm-diam rod pumped by 12 xenon flash lamps in a circular diffuse reflector configuration was determined to be 2.3%. This value for the depolarization as well as its radial profiles agree well with those determined from a cylindrically symmetric gain profile. In cases of deviation from the cylindrically symmetric pumping, the observed birefringence was found to be more for a clover leaf reflector as compared to that for a circular diffused reflector