Expressiveness and Robustness of First-Price Position Auctions

Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments

Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games

We study coordination mechanisms for Scheduling Games (with unrelated machines). In these games, each job represents a player, who needs to choose a machine for its execution, and intends to complete earliest possible. Our goal is to design scheduling policies that always admit a pure Nash equilibrium and guarantee a small price of anarchy for the l_k-norm social cost --- the objective balances overall quality of service and fairness. We consider policies with different amount of knowledge about jobs: non-clairvoyant, strongly-local and local. The analysis relies on the smooth argument together with adequate inequalities, called smooth inequalities. With this unified framework, we are able to prove the following results. First, we study the inefficiency in l_k-norm social costs of a strongly-local policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all deterministic, non-preemptive, strongly-local and non-waiting policies (non-waiting policies produce schedules without idle times). These results ensure that SPT is close to optimal with respect to the class of l_k-norm social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price of anarchy O(2^k). Second, we consider the makespan (l_infty-norm) social cost by making connection within the l_k-norm functions. We revisit some local policies and provide simpler, unified proofs from the framework's point of view. With the highlight of the approach, we derive a local policy Balance. This policy guarantees a price of anarchy of O(log m), which makes it the currently best known policy among the anonymous local policies that always admit a pure Nash equilibrium.Comment: 25 pages, 1 figur

Practice and problems regarding oral hygiene: study among female medical undergraduate students of tertiary care hospital, Pune, India

Background:As a health provider to community, a doctor should himself be aware of his oral health and undergraduate medical students who are future health professionals should also be well aware of their dental hygiene. Hence with an aim to assess the practice and problems about dental hygiene amongst female medical undergraduate students, this study was planned. Objective of the study was to assess the practices and problems regarding oral hygiene among female undergraduate medical students and efforts taken by them to solve these problems.Method: A cross-sectional study was undertaken among female undergraduate medical students residing in a hostel of a medical college.Results: 56.7% girls were using soft tooth brush, 69.3% students change their tooth brush every 6 monthly and 63.3% of them were brushing only once in a day. 79.3% were rinsing teeth after snack or meal. The percentage of students who were using mouth wash and tongue cleaner was 27.3% and 52% respectively. Bad breath was faced by only 9.33% of students, 39.33% were having cavities and 49.33% were having problem of plaque. 25.3% had never visited dentist. Scaling was performed by only 24.7% students and among them only 1.33% did it 6 monthly. It was observed that students using mouth wash 22.2% had significantly less problem of bad breath as compared to students who were not using 6.7%. Significantly larger numbers of students, with problem of cavities were observed to use mouth wash 60% and floss 68% as compared to those who did had this complaint.Conclusion: The study highlights the fact that preventive behaviour among medical students increased after they experienced some or the other oral health problem for which they were advised to follow these preventive practices so that the severity and extent of the disease does not progress. Further research is required on a larger scale so that the ways to increase the promotive and preventive oral health practices can be identified (e.g. behaviour change communication) to prevent the occurrence of oral health problems.

Laser applications in medicine: studies at Centre for Advanced Technology

The article provides a brief overview of the work being carried out at Centre for Advanced Technology, Indore, on laser applications in medicine as well as on the development of medical laser systems

Pricing Multi-Unit Markets

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer's information and agents' valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with (symmetric) subadditive valuations, even in an incomplete-information setting and with uniform prices

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

Optical properties of small particles and composite materials

Optical properties of submicron size particles and other nanostructures are determined by two different physical effects. The electric field penetration and distribution has a strong frequency dependence due to Mie type resonances. Secondly, quantum size effects influence the spectra and interactions of various excitations like electrons, excitons and phonons. Interplay of these two types of effects gives rise to a variety of linear and nonlinear optical phenomena which have been investigated a great deal during the last few years. The materials of interest are small particles and other nanostructures of semiconductors and metals. The nonlinear optical phenomena such as optical phase conjugation by degenerate four wave mixing, optical Kerr effect, saturation of absorption and optical bistability have been investigated in these materials. A brief overview of the available experimental information and our present theoretical understanding will be presented