Other
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Matthew Cheung
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Princeton University
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Applications of Mathematical Ecology to Economic Theory and the Role of Heterogeneous Conditions
Applications of Mathematical Ecology to Economic Theory and the Role of Heterogeneous Conditions
Advisor: Simon Levin
Abstract:
Complex systems in human societies share myriad qualities with those in nature. From game theory to dynamical systems, mathematical modeling has long served to investigate the intricacies of such societies, both in economic contexts and in the sciences of ecology and evolutionary biology. Incorporating concepts across disciplines then functions to not only introduce novel applications but also develop a more holistic framework that neatly discrete fields would never accomplish individually. One such phenomenon common to both spheres of research is heterogeneity—diversity of the conditions for various agents interacting in a market or ecosystem. Human systems in vivo suffer from ever-exponentiating inequality, an urgent and contemporary issue posing obstacles to collective action on crises from climate change to epidemics to poverty. While increasingly studied and implemented into models in the ecological sciences, heterogeneity in the economics literature, however, is underexplored in complex dynamical systems and games. Inequality of opportunities, resources, and other advantages are rather elided by a priori assumptions of homogeneous actors with identical conditions, for the sake of simplicity and mathematical tractability. The impact of inequities on societal welfare and our capacity to solve collective action problems is thus poorly understood in such economic theory, demonstrating demand for an interdisciplinary approach that lends and communicates ideas from mathematical biology. This doctoral thesis attempts to investigate the role of economic heterogeneity in social system modeling by adapting concepts from ecology and evolutionary biology, with separate chapters dedicated to dynasty theory, public goods games, and spatial dynamic markets. Chapter 2 explores growth rate heterogeneity and inequality in a process of intergenerational wealth transfers. Chapter 3 analyzes how unequal budget constraints and conditions affect the capacity for social norms to foster collective action solutions in public goods games, with implications for communal welfare. Chapter 4 diverges from this static microeconomic approach to interrogate the consequences of spatial heterogeneity and diffusion for endogenous market cycles. These chapters cumulatively aim to develop cohesive modeling frameworks on disparities in economic conditions, for not only future avenues of inquiry, but an enriched understanding of the potential to solve exigent collective action problems of our time.