On Structured Models of Coordinating Systems
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Coordination is a fundamental game theoretic process that can be used to describe a wide range of interactions from language formation and political polarization to signaling mechanics and the evolution of cooperative behavior. Underpinning all of it is the simple idea that a player is better off using the same strategy as the players around it. Modeling this simple type of interaction can lead to a rich diversity of behaviors, but it also brings with it a range of challenges. Different models can treat these challenges differently, but every modeling decision that is made to overcome one challenge reveals another. In this work I present four models of coordinating systems: A simulation model, a discrete time dual model, an ODE model, and a non-local diffusion model. Each modeling method allows us to use a different set of mathematical tools to interpret and make predictions about the behavior of coordinating systems, and in this way, each model addresses a different set of modeling challenges. Of course, no model perfectly addresses every challenge, but when taken together, we can gain a better understanding of coordinating systems as a whole.