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

Dynamics of Profit-Sharing Games

An important task in the analysis of multiagent systems is to understand how groups of selfish players can form coalitions, i.e., work together in teams. In this paper, we study the dynamics of coalition formation under bounded rationality. We consider settings where each team’s profit is given by a concave function, and propose three profit-sharing schemes, each of which is based on the concept of marginal utility. The agents are assumed to be myopic, i.e., they keep changing teams as long as they can increase their payoff by doing so. We study the properties (such as closeness to Nash equilibrium or total profit) of the states that result after a polynomial number of such moves, and prove bounds on the price of anarchy and the price of stability of the corresponding games.