Resource Competition on Integral Polymatroids

We study competitive resource allocation problems in which players distribute their demands integrally on a set of resources subject to player-specific submodular capacity constraints. Each player has to pay for each unit of demand a cost that is a nondecreasing and convex function of the total allocation of that resource. This general model of resource allocation generalizes both singleton congestion games with integer-splittable demands and matroid congestion games with player-specific costs. As our main result, we show that in such general resource allocation problems a pure Nash equilibrium is guaranteed to exist by giving a pseudo-polynomial algorithm computing a pure Nash equilibrium.Comment: 17 page

Designing cost-sharing methods for Bayesian games

We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria, have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE).We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable because they are easy to implement and, as we show, induce dominant strategies for the players

Acceptability to patients, carers and clinicians of an mHealth platform for the management of Parkinson's disease (PD_Manager): study protocol for a pilot randomised controlled trial.

BACKGROUND: Parkinson's disease is a degenerative neurological condition causing multiple motor and non-motor symptoms that have a serious adverse effect on quality of life. Management is problematic due to the variable and fluctuating nature of symptoms, often hourly and daily. The PD_Manager mHealth platform aims to provide a continuous feed of data on symptoms to improve clinical understanding of the status of any individual patient and inform care planning. The objectives of this trial are to (1) assess patient (and family carer) perspectives of PD_Manager regarding comfort, acceptability and ease of use; (2) assess clinician views about the utility of the data generated by PD_Manager for clinical decision making and the acceptability of the system in clinical practice. METHODS/DESIGN: This trial is an unblinded, parallel, two-group, randomised controlled pilot study. A total of 200 persons with Parkinson's disease (Hoehn and Yahr stage 3, experiencing motor fluctuations at least 2 h per day), with primary family carers, in three countries (110 Rome, 50 Venice, Italy; 20 each in Ioannina, Greece and Surrey, England) will be recruited. Following informed consent, baseline information will be gathered, including the following: age, gender, education, attitudes to technology (patient and carer); time since Parkinson's diagnosis, symptom status and comorbidities (patient only). Randomisation will assign participants (1:1 in each country), to PD_Manager vs control, stratifying by age (1 ≤ 70 : 1 > 70) and gender (60% M: 40% F). The PD_Manager system captures continuous data on motor symptoms, sleep, activity, speech quality and emotional state using wearable devices (wristband, insoles) and a smartphone (with apps) for storing and transmitting the information. Control group participants will be asked to keep a symptom diary covering the same elements as PD_Manager records. After a minimum of two weeks, each participant will attend a consultation with a specialist doctor for review of the data gathered (by either means), and changes to management will be initiated as indicated. Patients, carers and clinicians will be asked for feedback on the acceptability and utility of the data collection methods. The PD_Manager intervention, compared to a symptom diary, will be evaluated in a cost-consequences framework. DISCUSSION: Information gathered will inform further development of the PD_Manager system and a larger effectiveness trial. TRIAL REGISTRATION: ISRCTN Registry, ISRCTN17396879 . Registered on 15 March 2017

Optimal cost sharing for resource selection games

Joint use of resources with usage-dependent cost raises the question: who pays how much? We study cost sharing in resource selection games where the strategy spaces are either singletons or bases of a matroid defined on the ground set of resources. Our goal is to design cost sharing protocols so as to minimize the resulting price of anarchy and price of stability. We investigate three classes of protocols: basic protocols guarantee the existence of at least one pure Nash equilibrium; separable protocols additionally require that the resulting cost shares only depend on the set of players on a resource; uniform protocols are separable and require that the cost shares on a resource may not depend on the instance, that is, they remain the same even if new resources are added to or removed from the instance. We find optimal basic and separable protocols that guarantee the price of stability and price of anarchy to grow logarithmically in the number of players, except for the case of matroid games induced by separable protocols where the price of anarchy grows linearly with the number of players. For uniform protocols we show that the price of anarchy is unbounded even for singleton games

Archaeological and chemical evidence for early salt production in China

Salt production and trade is thought to be critical to the development of all states and emergent empires. Until now, however, scientific evidence of early salt production has rarely been presented, and no studies of early Chinese salt production have provided unequivocal proof. Here, we report x-ray fluorescence, x-ray diffraction, and scanning electron microscopy (SEM) analyses that demonstrate that salt was the primary product during the first millennium before Christ (B.C.) at Zhongba in Central China. This work provides an early example of salt production discovered in China and presents a methodology for evaluating salt production sites in other regions