The Dyson and Coulomb Games

René Carmona, Mark Cerenzia, Aaron Zeff Palmer

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We introduce and investigate certain N player dynamic games on the line and in the plane that admit Coulomb gas dynamics as a Nash equilibrium. Most significantly, we find that the universal local limit of the equilibrium is sensitive to the chosen model of player information in one dimension but not in two dimensions. We also find that players can achieve game theoretic symmetry through selfish behavior despite non-exchangeability of states, which allows us to establish strong localized convergence of the N-Nash systems to the expected mean field equations when tested against locally optimal player ensembles, i.e., against those exhibiting the same local limit as the Nash-optimal ensemble. In one dimension, this convergence notably features a nonlocal-to-local transition in the population dependence of the N-Nash system.

Original languageEnglish (US)
Pages (from-to)2897-2949
Number of pages53
JournalAnnales Henri Poincare
Issue number9
StatePublished - Sep 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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