International Affairs and Mathematics
Mark Haggerty, Stefano Tijerina
Potlucks have many names: shared community dinners, faith suppers, “bring-a-dish” dinners, etc. They represent the desire to share food with other people and make new friends, sometimes learning about other cultures in the process. Not only does one have to decide what dish to bring, but one must also decide how large of a dish, if there will be a theme, and what course it will fit. For instance, if everyone brings side dishes, there will not be enough food for everyone, and if someone brings food that most of the group cannot eat, then feelings will be hurt on all sides. And in a way, having a potluck is similar to creating integration policies. Successful integration policies are fair to all people and take a “two-street” approach, while simultaneously being a collaborative affair.
This paper will first explore fixed point theory, including the Kakutani Fixed Point Theorem and Brouwer Fixed Point Theorem; fixed point theorems are a significant field of mathematics and have many well-known applications. One of these applications is game theory, which is the study of how rational actors make decisions in everyday situations. Building upon the mathematical aspects of the first few chapters and the basics of game theory, this paper aims to build its own game theory model called the “Potluck Metaphor” that will model several methods of integration in the European Union; context for the model will be provided by critiquing three primary integration models and a brief literature review of the related field. Starting off with a simple game theory model for a dinner party, this paper will then slowly expand these models to show their applicability to European integration policy on an organizational level and on a member-specific level.
Searing, Llewellyn, "From Points to Potlucks: An Exploration of Fixed Point Theorems with Applications to Game Theory Models of Successful Integration Practices" (2022). Honors College. 772.