Presented By: Colloquium Series - Department of Mathematics
Colloquium Seminar: Mathematical models of reputation, polarization, and cooperation
Mari Kawakatsu (U Penn)
Addressing contemporary problems of collective action—from pandemic management to climate change—requires that we understand the dynamic interplay between information and behavior. In this talk, I will discuss two models of cooperative behavior coupled with dynamics of information spread. In the first model, we will consider cooperation driven by the spread of social reputations. Using methods from evolutionary game theory and dynamical systems, we develop a mathematical model of cooperation that integrates a mechanistic description of how reputations spread through peer-to-peer gossip. We show that sufficiently long periods of gossip can stabilize cooperation by facilitating consensus about reputations. In the second model, we will examine the dynamics of prosociality under political polarization. We develop a stochastic model of game-theoretic opinion dynamics in a multi-dimensional space of political interests. We show that while increasing the diversity of interests can improve both cooperation and social cohesion, strong partisan bias reduces the effective dimensionality of the opinion space via self-sorting along party lines, yielding greater in-group cooperation at the cost of increasing polarization. Taken together, these studies contribute to our understanding of when and how communication and opinion contagion facilitate cooperation.
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