Borel Equivalence Relations and Game Theory (Or: How I Learned to Stop Worrying and Love Descriptive Set Theory)

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I will present a survey of several published and working papers from recent years (nearly all jointly composed with Yehuda John Levy). The focus will be on a common thread running through all of these papers, namely the surprising effectiveness of concepts from descriptive set theory in attaining results on measurable equilibrium existence in Bayesian games, stochastic games, graphical games, and more. In particular, the countable Borel equivalence relation hierarchy, which is deeply related to questions of measurability versus non-measurability, plays a central role here. A new result on the existence of measurable approximate Harsanyi (i.e., ex ante) equilibria in Bayesian games will also be presented.