Welfare and Revenue Guarantees for Competitive Bundling Equilibrium

We study equilibria of markets with $m$ heterogeneous indivisible goods and $n$ consumers with combinatorial preferences. It is well known that a competitive equilibrium is not guaranteed to exist when valuations are not gross substitutes. Given the widespread use of bundling in real-life markets, we study its role as a stabilizing and coordinating device by considering the notion of \emph{competitive bundling equilibrium}: a competitive equilibrium over the market induced by partitioning the goods for sale into fixed bundles. Compared to other equilibrium concepts involving bundles, this notion has the advantage of simulatneous succinctness ($O(m)$ prices) and market clearance. Our first set of results concern welfare guarantees. We show that in markets where consumers care only about the number of goods they receive (known as multi-unit or homogeneous markets), even in the presence of complementarities, there always exists a competitive bundling equilibrium that guarantees a logarithmic fraction of the optimal welfare, and this guarantee is tight. We also establish non-trivial welfare guarantees for general markets, two-consumer markets, and markets where the consumer valuations are additive up to a fixed budget (budget-additive). Our second set of results concern revenue guarantees. Motivated by the fact that the revenue extracted in a standard competitive equilibrium may be zero (even with simple unit-demand consumers), we show that for natural subclasses of gross substitutes valuations, there always exists a competitive bundling equilibrium that extracts a logarithmic fraction of the optimal welfare, and this guarantee is tight. The notion of competitive bundling equilibrium can thus be useful even in markets which possess a standard competitive equilibrium

On the Efficiency of All-Pay Mechanisms

We study the inefficiency of mixed equilibria, expressed as the price of anarchy, of all-pay auctions in three different environments: combinatorial, multi-unit and single-item auctions. First, we consider item-bidding combinatorial auctions where m all-pay auctions run in parallel, one for each good. For fractionally subadditive valuations, we strengthen the upper bound from 2 [Syrgkanis and Tardos STOC'13] to 1.82 by proving some structural properties that characterize the mixed Nash equilibria of the game. Next, we design an all-pay mechanism with a randomized allocation rule for the multi- unit auction. We show that, for bidders with submodular valuations, the mechanism admits a unique, 75% efficient, pure Nash equilibrium. The efficiency of this mechanism outperforms all the known bounds on the price of anarchy of mechanisms used for multi-unit auctions. Finally, we analyze single-item all-pay auctions motivated by their connection to contests and show tight bounds on the price of anarchy of social welfare, revenue and maximum bid.Comment: 26 pages, 2 figures, European Symposium on Algorithms(ESA) 201

First E region observations of mesoscale neutral wind interaction with auroral arcs

We report the first observations of E region neutral wind fields and their interaction with auroral arcs at mesoscale spatial resolution during geomagnetically quiet conditions at Mawson, Antarctica. This was achieved by using a scanning Doppler imager, which can observe thermospheric neutral line-of-sight winds and temperatures simultaneously over a wide field of view. In two cases, the background E region wind field was perpendicular to an auroral arc, which when it appeared caused the wind direction within ∼50 km of the arc to rotate parallel along the arc, reverting to the background flow direction when the arc disappeared. This was observed under both westward and eastward plasma convection. The wind rotations occurred within 7–16 min. In one case, as an auroral arc propagated from the horizon toward the local zenith, the background E region wind field became significantly weaker but remained unaffected where the arc had not passed through. We demonstrate through modeling that these effects cannot be explained by height changes in the emission layer. The most likely explanation seems to be the greatly enhanced ion drag associated with the increased plasma density and localized ionospheric electric field associated with auroral arcs. In all cases, the F region neutral wind appeared less affected by the auroral arc, although its presence is clear in the data

Characterizing Vickrey allocation rule by anonymity

We consider the problem of allocating finitely many units of an indivisible good among a group of agents when each agent receives at most one unit of the good and pays a non-negative price. For example, imagine that a government allocates a fixed number of licenses to private firms, or that it distributes equally divided lands to households. Anonymity in welfare is a condition of impartiality in the sense that it requires allocation rules to treat agents equally in welfare terms from the viewpoint of agents who are ignorant of their own valuations or identities. We show that the Vickrey allocation rule is the unique allocation rule satisfying strategy-proofness, anonymity in welfare, and individual rationality

Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case

While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions

Decentralized subcontractor scheduling with divisible jobs

Subcontracting allows manufacturer agents to reduce completion times of their jobs and thus obtain savings. This paper addresses the coordination of decentralized scheduling systems with a single subcontractor and several agents having divisible jobs. Assuming complete information, we design parametric pricing schemes that strongly coordinate this decentralized system, i.e., the agents’ choices of subcontracting intervals always result in efficient schedules. The subcontractor’s revenue under the pricing schemes depends on a single parameter which can be chosen to make the revenue as close to the total savings as required. Also, we give a lower bound on the subcontractor’s revenue for any coordinating pricing scheme. Allowing private information about processing times, we prove that the pivotal mechanism is coordinating, i.e., agents are better off by reporting their true processing times, and by participating in the subcontracting. We show that the subcontractor’s maximum revenue with any coordinating mechanism under private information equals the lower bound of that with coordinating pricing schemes under complete information. Finally, we address the asymmetric case where agents obtain savings at different rates per unit reduction in completion times. We show that coordinating pricing schemes do not always exist in this case

The development and validation of the Dementia Quality of Life Scale for Older Family Carers (DQoL-OC)

Purpose: Little is known about how caregiving affects the quality of life (QoL) of older family carers and no dementia and age-specific QoL scale is available for use with this population. This study aimed to develop and validate a unique dementia caregiving- and age-specific tool – the ‘Dementia Quality of Life Scale for Older Family Carers’ (DQoL-OC). Methods: The scale items were identified in focus groups with older family carers in the UK. Content and face validity were evaluated by a panel of six experts. A set of 100 items assessed on a 5-point Likert scale was tested with 182 older family carers. Test–re-test reliability was conducted with 18 individuals. Exploratory factor analysis was used to identify the QoL model and reduce the number of scale items. Convergent construct validity and internal consistency were also established. Results: A one-factor solution containing 22 items was obtained. Test–re-test reliability (lower bound r = 0.835; p < 0.001), internal consistency (Cronbach's α = 0.936), and convergent construct validity were established. Significantly lower levels of QoL were found in female older carers; those who perceived their relatives with dementia as being at the earlier stages of the disease and with unstable dementia symptoms; those providing care more hours per day and more days per week; and those in younger-old age. Conclusions: The DQoL-OC is a valid and reliable scale that will be useful for research and in clinical practice with older family carers of people with dementia. These study results will inform future health and social care aiming to improve life quality for this overlooked population of carers

Transient activation of dopaminergic neurons during development modulates visual responsiveness, locomotion and brain activity in a dopamine ontogeny model of schizophrenia

It has been observed that certain developmental environmental risk factors for schizophrenia when modeled in rodents alter the trajectory of dopaminergic development, leading to persistent behavioural changes in adults. This has recently been articulated as the "dopamine ontogeny hypothesis of schizophrenia". To test one aspect of this hypothesis, namely that transient dopaminergic effects during development modulate attention-like behavior and arousal in adults, we turned to a small-brain model, Drosophila melanogaster. By applying genetic tools allowing transient activation or silencing of dopaminergic neurons in the fly brain, we investigated whether a critical window exists during development when altered dopamine (DA) activity levels could lead to impairments in arousal states in adult animals. We found that increased activity in dopaminergic neurons in later stages of development significantly increased visual responsiveness and locomotion, especially in adult males. This misallocation of visual salience and hyperactivity mimicked the effect of acute methamphetamine feeding to adult flies, suggesting up-regulated DA signaling could result from developmental manipulations. Finally, brain recordings revealed significantly reduced gamma-band activity in adult animals exposed to the transient developmental insult. Together, these data support the idea that transient alterations in DA signaling during development can permanently alter behavior in adults, and that a reductionist model such as Drosophila can be used to investigate potential mechanisms underlying complex cognitive disorders such as schizophrenia