Wang, Guanyi; (2025) Essays on Individualized Treatment Allocation and Network Spillover. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis explores optimal individualized treatment allocation in social network settings. The first chapter studies the individualized vaccine allocation under limited supply within a heterogeneous SIR network framework, leveraging social network data containing individual demographic characteristics and health status. By exploiting submodularity of the allocation problem, it devises a novel greedy algorithm to assign the treatment, with theoretical performance guarantees. Simulation results underline the importance of accounting for spillover effects when targeting vaccinations. The second chapter focuses on treatment allocation in sequential decision games of interacting agents, where stationary distributions of outcomes follow Gibbs distributions. To overcome the analytical and computational challenges of direct optimization, it employs a variational approximation to characterize and estimate optimal treatment policies. I characterize the performance of the variational approximation, deriving a performance guarantee for the greedy optimization algorithm via a welfare regret bound. I implement our proposed method in simulation exercises and an empirical application using the Indian microfinance data (Banerjee et al., 2013), and show it delivers significant welfare gains. The third chapter examines treatment allocation in large-scale simultaneous decision games with strategic complementarities. I introduce a maximin optimal treatment allocation rule that remains robust to the presence of multiple Nash equilibria. Remaining agnostic about the specific selection rule, I derive a closed-form expression for the boundary of the identified set of equilibrium outcomes. To address the incompleteness that emerges from unspecified selection, I propose a policy maximizing worst-case welfare. A greedy algorithm is used for implementation, with theoretical performance guarantees established through a welfare regret bound that accounts for both sampling uncertainty and the use of a greedy algorithm. Finally, I demonstrate this method with an application to the microfinance dataset of Banerjee et al. (2013).

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