Social Welfare in One-sided Matching Markets without Money

We study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent's utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation. We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526, 2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first non-trivial performance guarantees for these natural mechanisms

Current use of baseline medical treatment in chronic rhinosinusitis: Data from the National Chronic Rhinosinusitis Epidemiology Study (CRES)

Objectives: According to clinical and comissioning guidelines for chronic rhinosinusitis (CRS), patients being referred to secondary care should have failed primary medical treatment with nasal douching (ND) and intranasal corticosteroids (INCS). The study objectives were to identify the rate of specific medical therapy in CRS patients and establish any differences in medication use, for both CRS and associated medical conditions, between CRS phenotypes.  Design and setting: Case-control study in a secondary care setting.  Methods: Participant-reported study-specific questionnaire capturing free text data on current medication use at the time of study entry. Qualitative interviews with 21 participants also explored their experience of CRS and its management.  Particpants: Patients with both without (CRSsNPs) and with polyps (CRSwNPs). Main outcome measuresReported use of CRS-related and non-related medications.ResultsWithin a total of 1243 CRS participants, current INCS usage was low (18% in CRSwNPs, 12% in CRSsNPs); ND was being performed by only 1% of all participants. Bronchodilators and inhaled corticosteroids use was significantly higher in CRSwNPs participants (p < 0.0001). Antidepressants use was significantly higher in CRSsNPs (14% versus 7%, p < 0.0002). There were no significant regional variations in rates of INCS use, nor any significant influence of social deprivation.  Conclusions: The current use of baseline medical therapy in CRS appears to be very low, representing a combination of poor patient compliance, possible ineffectiveness of treatment and a lack of familiarity with current guidelines amongst general practitioners and some ENT specialists. Work is needed to disseminate guidelines to all practitioners involved and reduce unnecessary burden on existing healthcare resources for this common condition by ensuring timely referral and definitive management

Commons with increasing marginal costs: random priority versus average cost

ndivisible units are produced with increasing marginal costs. Under average cost, each user pays average cost. Under random priority, users are randomly ordered (without bias) and successively offered to buy at the true marginal cost. Both average cost (AC) and random priority (RP) inefficiently overproduce. RP tends to overproduce less, but which game collects more surplus depends much on the demand configuration. We show that a key to compare the welfare properties of the two mechanisms is the crowding factor, i.e., the number of potential users over the number of units of output users can afford: The more crowded the commons, the more RP outperforms AC. In the quadratic cost case, beyond the threshold value of 2.4 for the crowding factor, RP strongly outperforms AC; beneath it AC only mildly outperforms RP. Thus the RP mechanism manages crowded commons better than AC

Symmetry in Models with Pure and Almost Pure Individual Risks

This paper investigate the existence of asymmetric equilibria in a pure exchange economy with individual risks. The model is an extension of Malinvaud's (1973). Agents face identical pure individual risks: their endowments and utility functions only depend on their individual state; but there exists one good for which some aggregate component of the risk is introduced through endowments: individual risks are 'almost pure'.GENERAL EQUILIBRIUM ; RISK