Efficiency of Truthful and Symmetric Mechanisms in One-sided Matching

We study the efficiency (in terms of social welfare) of truthful and symmetric mechanisms in one-sided matching problems with {\em dichotomous preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are particularly interested in the well-known {\em Random Serial Dictatorship} mechanism. For dichotomous preferences, we first show that truthful, symmetric and optimal mechanisms exist if intractable mechanisms are allowed. We then provide a connection to online bipartite matching. Using this connection, it is possible to design truthful, symmetric and tractable mechanisms that extract 0.69 of the maximum social welfare, which works under assumption that agents are not adversarial. Without this assumption, we show that Random Serial Dictatorship always returns an assignment in which the expected social welfare is at least a third of the maximum social welfare. For normalized von Neumann-Morgenstern preferences, we show that Random Serial Dictatorship always returns an assignment in which the expected social welfare is at least \frac{1}{e}\frac{\nu(\opt)^2}{n}, where \nu(\opt) is the maximum social welfare and $n$ is the number of both agents and items. On the hardness side, we show that no truthful mechanism can achieve a social welfare better than \frac{\nu(\opt)^2}{n}.Comment: 13 pages, 1 figur

Size versus truthfulness in the house allocation problem

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomized mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomized mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of eovere-1. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 18 over 13 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. In the case that the mechanism must additionally be non-bossy, an improved lower bound of eovere-1 holds. This lower bound is tight given that RSDM for strict preference lists is non-bossy. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomized strategy of the administrator who interviews the applicants

Social welfare in one-sided matchings: Random priority and beyond

We study the problem of approximate social welfare maximization (without money) in one-sided matching problems when agents have unrestricted cardinal preferences over a finite set of items. Random priority is a very well-known truthful-in-expectation mechanism for the problem. We prove that the approximation ratio of random priority is Theta(n^{-1/2}) while no truthful-in-expectation mechanism can achieve an approximation ratio better than O(n^{-1/2}), where n is the number of agents and items. Furthermore, we prove that the approximation ratio of all ordinal (not necessarily truthful-in-expectation) mechanisms is upper bounded by O(n^{-1/2}), indicating that random priority is asymptotically the best truthful-in-expectation mechanism and the best ordinal mechanism for the problem.Comment: 13 page

Social Welfare in One-Sided Matching Mechanisms

We study the Price of Anarchy of mechanisms for the well-known problem of one-sided matching, or house allocation, with respect to the social welfare objective. We consider both ordinal mechanisms, where agents submit preference lists over the items, and cardinal mechanisms, where agents may submit numerical values for the items being allocated. We present a general lower bound of $\Omega(\sqrt{n})$ on the Price of Anarchy, which applies to all mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and Random Priority, achieve a matching upper bound. We extend our lower bound to the Price of Stability of a large class of mechanisms that satisfy a common proportionality property, and show stronger bounds on the Price of Anarchy of all deterministic mechanisms

Awareness of COVID-19 outbreak in local population of Maval taluka in Maharashtra, India

Background: There is a growing fear and perceived threat about coronavirus among local population. The population, inclusive of all age groups is making use of available media such as internet, social media, newspapers and television to make themselves aware. There is no authenticity and information may be wrong. Since, corona has become major cause of concern, present study was carried out to bring the awareness and educate them about coronavirus among the local population.Methods: A cross sectional study was carried out on COVID-19 by using online Google based questionnaire in Maval area to assess the knowledge and awareness about corona virus among the 125 local participants. The questionnaire consisted of 10 validated peer reviewed questions covering various aspects of COVID-19 awareness were voluntarily filled by participants. Data was analysed in Microsoft Excel 2010.Results: Present findings revealed that 94% participants knew that COVID-19 is caused by the corona was first detected in Wuhan China and the first case of the same was reported in Kerala was known to 60% respondents. The virus remains on the surface of mobiles was known to 11% participants.76.8% participants apprised 2-14 days being the incubation period of the virus. Patients with two or more comorbidities can develop severe COVID-19 was known to 46.6% participants. Only 5% participants knew the difference between swine flu and corona virus. Nearly 89% participants knew soap is the best material for cleaning in the presence of dirt and about 51% participants knew the need of isolating persons with known COVID- 19 infection.Conclusions: Correct answers with scientific explanation were posted to the participants in the form of instantaneous feedback. Hence knowledge gained was increased by the participants. Their misconceptions were removed. More awareness can be brought & propagation of COVID-19 infection can be prevented even after lockdown period