Empirical centroid fictitious play: An approach for distributed learning in multi-agent games

Brian Swenson, Soummya Kar, Joao Xavier

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


The paper is concerned with distributed learning in large-scale games. The well-known fictitious play (FP) algorithm is addressed, which, despite theoretical convergence results, might be impractical to implement in large-scale settings due to intense computation and communication requirements. An adaptation of the FP algorithm, designated as the empirical centroid fictitious play (ECFP), is presented. In ECFP players respond to the centroid of all players' actions rather than track and respond to the individual actions of every player. Convergence of the ECFP algorithm in terms of average empirical frequency (a notion made precise in the paper) to a subset of the Nash equilibria is proven under the assumption that the game is a potential game with permutation invariant potential function. A more general formulation of ECFP is then given (which subsumes FP as a special case) and convergence results are given for the class of potential games. Furthermore, a distributed formulation of the ECFP algorithm is presented, in which, players endowed with a (possibly sparse) preassigned communication graph, engage in local, non-strategic information exchange to eventually agree on a common equilibrium. Convergence results are proven for the distributed ECFP algorithm.

Original languageEnglish (US)
Article number7109924
Pages (from-to)3888-3901
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number15
StatePublished - Aug 1 2015

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


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