On best-response dynamics in potential games

Brian Swenson, Ryan William Murray, Soummya Kar

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


The paper studies the convergence properties of (continuous-time) best-response dynamics from game theory. Despite their fundamental role in game theory, best-response dynamics are poorly understood in many games of interest due to the discontinuous, set-valued nature of the best-response map. The paper focuses on elucidating several important properties of best-response dynamics in the class of multiagent games known as potential games—a class of games with fundamental importance in multiagent systems and distributed control. It is shown that in almost every potential game and for almost every initial condition, the best-response dynamics (i) have a unique solution, (ii) converge to pure-strategy Nash equilibria, and (iii) converge at an exponential rate.

Original languageEnglish (US)
Pages (from-to)2734-2767
Number of pages34
JournalSIAM Journal on Control and Optimization
Issue number4
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


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