Mathematica code for the topological analysis of Thom’s Catastrophes in 2 × 2 economic games

Abstract

<p>René Thom’s work on topological instabilities applied new methods to questions of dynamical stability that traditionally belonged to the domain of dynamical systems theorists. Topological instability focuses on universal properties of bifurcations in systems where multiple equilibria form and disappear as a function of system parameters. However, the complete mathematical description is quite abstract and the analysis benefits from graphical intuitions. Here we provide the code, in the form of a Mathematica notebook, used in our recent Games and Economic Behaviour paper (Harriset al., 2023). It illustrates our main results providing the intuition necessary to explore the bifurcations in the formal proofs.</p>