The literature on algorithmic mechanism design is mostly concerned with game-theoretic versions of optimization problems to which standard economic money-based mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on payments. In this paper, we advocate the reconsideration of highly structured optimization problems in the context of mechanism design. We explicitly argue for the first time that, in such domains, approximation can be leveraged to obtain truthfulness without resorting to payments. This stands in contrast to previous work where payments are almost ubiquitous, and (more often than not) approximation is a necessary evil that is required to circumvent computational complexity.We present a case study in approximate mechanism design without money. In our basic setting agents are located on the real line and the mechanism must select the location of a public facility; the cost of an agent is its distance to the facility. We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective functions: the social cost, and the maximum cost. We then extend our results in two natural directions: a domain where two facilities must be located, and a domain where each agent controls multiple locations.

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BackgroundRegular physical activity is known to be beneficial for people with type 2 diabetes. Nevertheless, most of the people who have diabetes lead a sedentary lifestyle. Smartphones create new possibilities for helping people to adhere to their physical activity goals through continuous monitoring and communication, coupled with personalized feedback.ObjectiveThe aim of this study was to help type 2 diabetes patients increase the level of their physical activity.MethodsWe provided 27 sedentary type 2 diabetes patients with a smartphone-based pedometer and a personal plan for physical activity. Patients were sent short message service messages to encourage physical activity between once a day and once per week. Messages were personalized through a Reinforcement Learning algorithm so as to improve each participant’s compliance with the activity regimen. The algorithm was compared with a static policy for sending messages and weekly reminders.ResultsOur results show that participants who received messages generated by the learning algorithm increased the amount of activity and pace of walking, whereas the control group patients did not. Patients assigned to the learning algorithm group experienced a superior reduction in blood glucose levels (glycated hemoglobin [HbA1c]) compared with control policies, and longer participation caused greater reductions in blood glucose levels. The learning algorithm improved gradually in predicting which messages would lead participants to exercise.ConclusionsMobile phone apps coupled with a learning algorithm can improve adherence to exercise in diabetic patients. This algorithm can be used in large populations of diabetic patients to improve health and glycemic control. Our results can be expanded to other areas where computer-led health coaching of humans may have a positive impact. Summary of a part of this manuscript has been previously published as a letter in Diabetes Care, 2016.

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