Game-Theoretically Allocating Resources to Catch Evaders and Payments to Stabilize Teams

Allocating resources optimally is a nontrivial task, especially when multiple

self-interested agents with conflicting goals are involved. This dissertation

uses techniques from game theory to study two classes of such problems:

allocating resources to catch agents that attempt to evade them, and allocating

payments to agents in a team in order to stabilize it. Besides discussing what

allocations are optimal from various game-theoretic perspectives, we also study

how to efficiently compute them, and if no such algorithms are found, what

computational hardness results can be proved.

The first class of problems is inspired by real-world applications such as the

TOEFL iBT test, course final exams, driver's license tests, and airport security

patrols. We call them test games and security games. This dissertation first

studies test games separately, and then proposes a framework of Catcher-Evader

games (CE games) that generalizes both test games and security games. We show

that the optimal test strategy can be efficiently computed for scored test

games, but it is hard to compute for many binary test games. Optimal Stackelberg

strategies are hard to compute for CE games, but we give an empirically

efficient algorithm for computing their Nash equilibria. We also prove that the

Nash equilibria of a CE game are interchangeable.

The second class of problems involves how to split a reward that is collectively

obtained by a team. For example, how should a startup distribute its shares, and

what salary should an enterprise pay to its employees. Several stability-based

solution concepts in cooperative game theory, such as the core, the least core,

and the nucleolus, are well suited to this purpose when the goal is to avoid

coalitions of agents breaking off. We show that some of these solution concepts

can be justified as the most stable payments under noise. Moreover, by adjusting

the noise models (to be arguably more realistic), we obtain new solution

concepts including the partial nucleolus, the multiplicative least core, and the

multiplicative nucleolus. We then study the computational complexity of those

solution concepts under the constraint of superadditivity. Our result is based

on what we call Small-Issues-Large-Team games and it applies to popular

representation schemes such as MC-nets.

Neurosurgical Needs and Assets Assessment of Public Hospitals in Uganda: An Eevaluation of Mulago Hospital to Inform Neurosurgical Program Planning at Mbarara

Background: Since 2007, there has been an ongoing collaboration between Duke University and Mulago National Referral Hospital (NRH) in Kampala, Uganda to increase surgical capacity. This program is prepared to expand to other sites within Uganda to improve neurosurgery outside of Kampala as well. This study assessed the existing progress at Mulago NRH and the neurosurgical needs and assets at two potential sites for expansion. Methods: Three public hospitals were visited to assess needs and assets: Mulago NRH, Mbarara Regional Referral Hospital (RRH), and Gulu RRH. At each site, a surgical capacity tool was administered and healthcare workers were interviewed about perceived needs and assets. A total of 39 interviews were conducted between the three sites. Thematic analysis of the interviews was conducted to identify the reported needs and assets at each hospital. Results: Some improvements are needed to the Duke-Mulago Collaboration model prior to expansion; minor changes to the neurosurgery residency program as well as the method for supply donation and training provided during neurosurgery camps need to examined. Neurosurgery can be implemented at Mbarara RRH currently but the hospital needs a biomedical equipment technician on staff immediately. Gulu RRH is not well positioned for Neurosurgery until there is a CT Scanner somewhere in the Northern Region of Uganda or at the hospital. Conclusions: Neurosurgery is already present in Uganda on a small scale and needs rapid expansion to meet patient needs. This progression is possible with prudent allocation of resources on strategic equipment purchases, human resources including clinical staff and biomedical staff, and changes to the supply chain management system.

Protected Areas' Impacts on Brazilian Amazon Deforestation: Examining Conservation-Development Interactions to Inform Planning.

Protected areas are the leading forest conservation policy for species and ecoservices goals and they may feature in climate policy if countries with tropical forest rely on familiar tools. For Brazil's Legal Amazon, we estimate the average impact of protection upon deforestation and show how protected areas' forest impacts vary significantly with development pressure. We use matching, i.e., comparisons that are apples-to-apples in observed land characteristics, to address the fact that protected areas (PAs) tend to be located on lands facing less pressure. Correcting for that location bias lowers our estimates of PAs' forest impacts by roughly half. Further, it reveals significant variation in PA impacts along development-related dimensions: for example, the PAs that are closer to roads and the PAs closer to cities have higher impact. Planners have multiple conservation and development goals, and are constrained by cost, yet still conservation planning should reflect what our results imply about future impacts of PAs.