On the Convergence of Piecewise Linear Strategic Interaction Dynamics on Networks

Bahman Gharesifard, Behrouz Touri, Tamer Basar, Jeff Shamma

Research output: Contribution to journalArticlepeer-review


We prove that the piecewise linear best-response dynamical systems of strategic interactions are asymptotically convergent to their set of equilibria on any weighted undirected graph. We study various features of these dynamical systems, including the uniqueness and abundance properties of the set of equilibria and the emergence of unstable equilibria. We also introduce the novel notions of social equivalence and social dominance on directed graphs, and demonstrate some of their interesting implications, including their correspondence to consensus and chromatic number of partite graphs. Examples illustrate our results.

Original languageEnglish (US)
Article number7258336
Pages (from-to)1682-1687
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Jun 2016


  • Best-response dynamics
  • Nash equilibria
  • distributed algorithms
  • games on networks

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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