I am an applied mathematician studying individual behavior in biological and sociological systems, with a recent focus on modeling rational individual behavior during an epidemic using epidemic game theory. I am also interested in modeling the development of human societies to better understand the development of institutions and their interplay with individual behaviors and relations.

Epidemic Game Theory

My dissertation work, which I did under the supervision of Tim Reluga, was primarily focused on establishing uniqueness of Nash equilibria in certain epidemic games. The first of these was the SI variant of the social distancing game. Social distancing games are a class of epidemic game which models individual self-quarantining behaviors. It is folk-belief that the Nash equilibria in simple variants of these games is unique, but a conclusion proof has yet to assert this fact in general. I was able to prove uniqueness in the social distancing game subject to a conventional SI epidemic dynamic. This result extends to any future cost discount rate, so every outlook from perfect future-looking to completely myopic has a unique Nash equilibrium strategy. I am currently working on extending the argument to other variants of the social distancing game.

The other epidemic game I developed, inspired by diseases like cholera, is the environmental distancing game. While similar in structure to the social distancing them, this game is distinguished by having two sources of infection, host-to-host and an environmental vector, where only the latter pathway is controlled. I demonstrated that this game exhibits multiple Nash equilibria, thus finding a clear example where uniqueness breaks down. When considered with positive discount rates, this game also exhibits very strange, non-monotone, equilibria, which is counter-intuitive given the monotone increasing risk of infection.

Currently, I am working on publishing my epidemic game work, and am also exploring other extensions of these games. I am particularly interested in the effects of population contact structure on rational equilibrium behaviors, especially when the population contacts are heterogeneous. Epidemic games are generally built upon SIR-type models, so populations are assumed to be mass-action mixed. As my own work with smallpox modeling demonstrated, human populations can be connected following a fat-tailed distributions. Taking this reality into account could have significant implications for the structure of rational behavior.

Development of Institutions

Human institutions play a significant role in the proper functioning of modern societies. These institutions have developed across centuries into their current forms, and will continue to develop going forward. Currently, I am interested in two aspects of institutions and the role in society. The first is building upon work by economists Greif, Mokyr, and Tabellini, on the difference in historical development of Europe and China. They argue that a key aspect of these societies which led to different trajectories was the different fundamental social arrangements these societies have, China being structured around kin relations while Europe was more corporate structured. This thesis, which they support with a thorough economic analysis, is related to Henrich’s WEIRD psychology thesis about Europeans. I am working on constructing mathematical models which elucidate how different social structures lead to distinct institutional development.

The second aspect I am exploring is the relation between institutions and individual behavior. One interpretation of non-uniqueness in the environmental distancing game is that effective institutions do not inherently alter behavior in a beneficial manner. Instead, societies are subject to a burden of history, where the behavior they exhibit influences the equilibrium they converge toward. This has both a beneficial and a detrimental side. A society who already adopts the beneficial behavior will maintain it even as the institution worsens, while a society that behaves in a non-beneficial fashion requires very effective institutions to alter this behavior. What is key to this situation is the institution requires the population to adopt a certain behavior for their intervention to be effective, but it isn’t inherent that having a potentially effective institution leads to the adoption of this behavior. While this current insight is specific to this epidemic game with a certain type of institutional response, I am exploring the general relation between an institution and the behavior of the population to further investigate how generic this structure is.