Author ORCID Identifier

https://orcid.org/0000-0002-4739-9018

Date of Award

Spring 6-14-2025

Document Type

Thesis (Ph.D.)

Department or Program

Mathematics

First Advisor

Feng Fu

Second Advisor

Scott Pauls

Third Advisor

Dimitrios Giannakis

Abstract

The natural world abounds with examples of complex behavior in humans and many other species. Evolutionary game theory is a powerful mathematical framework to understand the origins of many such behaviors like cooperation. Since these behaviors are often selected against initially, understanding why they are so widespread has been a longstanding question. Rather than assuming agents' rationality, like in traditional game theory, this approach studies the mutation and selection of strategies themselves. However most behavior is neither perfectly rational nor entirely determined by genetics. This dissertation works to bridge the gap between these two perspectives by analyzing models where individuals follow a variety of approaches to learning their strategy. One series of models characterizes the stability of equilibria in the notoriously intractable issue of exploration vs exploitation, consider constant, frequency, and time dependent selection. We extend this to groups of agents who simultaneously learn from their surroundings, advancing theory for a Machine Learning method combining Reinforcement Learning with Genetic Algorithms. We then examine agents that consider general types of norms, finding examples the can and cannot promote cooperation. Lastly we find the counter-intuitive effect that introducing trivial topics can completely change whether a population will polarize or reach consensus, based on an opinion dynamics model where agents partially adopt the behavior of those around them. Taken together, these results improve our understanding of why particular behaviors have spread so successfully. This goal of understanding and optimizing behavior has applications to many fields, from biology, computer science, and economics, to psychology, ecology, and sociology. Several open questions remain, making evolutionary game theory a promising area for future research with broad scientific impacts. As we see rapid shifts in society brought on by advances in artificial intelligence and changes to the political and literal climate, it becomes increasingly important to understand how to foster cooperation within and between communities.

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