Unified convergence proofs of continuous-time fictitious play

Jeff S. Shamma*, Gurdal Arslan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


We consider a continuous-time version of fictitious play (FP), in which interacting players evolve their strategies in reaction to their opponents' actions without knowledge of their opponents' utilities. It is known that FP need not converge, but that convergence is possible in certain special cases including zero-sum games, identical interest games, and two-player/two-move games. We provide a unified proof of convergence in all of these cases by showing that a Lyapunov function previously introduced for zero-sum games also can establish stability in the other special cases. We go on to consider a two-player game in which only one player has two-moves and use properties of planar dynamical systems to establish convergence.

Original languageEnglish (US)
Pages (from-to)1137-1142
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number7
StatePublished - Jul 2004
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received October 17, 2003. Recommended by Associate Editor C. D. Charalambous. This work was supported by the Air Force Office of Scientific Research/MURI under Grant F49620-01-1-0361 and by summer support by the UF Graduate Engineering Research Center.

ASJC Scopus subject areas

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


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